But should the Reds sell him and what disciplinary action - if any - should be taken? Our experts - including Graeme Souness and Jamie Redknapp - have their say...
Phil Thompson, Liverpool 1971-84
"It was disgraceful and it is bringing Liverpool Football Club into disrepute. You can't argue with a lot of things that people have said about Luis Saurez and the football club and we all know he did it at Ajax when he was playing in Holland. It is a massive worry and it's great that Liverpool have learned from the Patrice Evra racism problem that we had last season and have come out and issued apologies. I was waiting last night for apologies and Luis Suarez has done it and the club has done it and now he's been fined. It should probably be in the region of two week's wages and rightly so.
"Anger management is right, he needs it. A lot of the top players have anger in them and that's what makes them good players. Sometimes with Luis he tips the balance, he has had two episodes with biting and it's outrageous; it's something we can't have. I love Luis Suarez as a footballer playing for my football club, but you just cannot have this. It's absolutely unbelievable. I would like to see maybe a psychologist because you have to look deeper with this guy. Why does he do such a thing? If he'd done it once you could say it was an instinctive thing, but doing it twice it absolutely amazing. He does need help, and he needs understanding. He will be slapped with a massive fine, but we have to look deeper into why this guy has done this.
"The owners are big, big players now. How will they view this? What is their vision for Liverpool Football Club? Is it to be presented in the right way worldwide because we are an institution worldwide? The way I look at it is they sacked Kenny Dalglish and if you can sack Kenny Dalglish I suppose they can sack anybody at Liverpool Football Club."
David Fairclough, Liverpool 1974-83
"This has besmirched Liverpool's name - the club certainly doesn't want to be in the news for this type of thing and it's unfortunate that once again Luis Suarez is the victim. But he's the best player in the team at the moment; he's one of the top players in the world; his ability is unquestioned and his performances, generally this season, have been top class. So it would be a little extreme of Liverpool to wipe their hands of him and send him packing. Obviously, a lot of thought has to go into the incident and I'm sure there will be a number of discussions. Clearly Luis needs a little bit of help - he has an anger issue, I suspect. That's his drive to win and compete but it's a little bit extreme. I think Liverpool have to try and work with Luis Suarez. He's shown improvement in other ways over the last 18-24 months and hopefully they can find a suitable solution.
"Managers like Bill Shankly and Bob Paisley would have admired his competitiveness and his undying determination to get the right result for Liverpool, but it's very difficult to say exactly how they would have reacted to this. I don't think they would have sweepingly said 'that's the end' and wipe their hands of Luis Suarez. We respect Luis Suarez for his attitude and determination and his football ability but he clearly needs a little bit of help. There has been such a dramatic reaction to this event that I think there is a bit of a rush to put a guilty verdict on his shoulders."
Tony Cascarino, Chelsea 1992-1994
"Liverpool did know that they were buying a player who had bit an opponent - he's got previous. Everyone is talking about the club's reputation but they did decide to buy him after he had done this in Dutch football. It will never look good and people will talk about the image of football, which suffered yesterday. If Luis Suarez was an average player, he'd be out of the club - they would sell him - but they are not going to sell him because every club in the world would want him. So Liverpool will stand strong and initially they will do everything in their power to try and make Luis Suarez conscious that this sort of behaviour is unacceptable and won't happen again. But they will keep him and then they'll back him. There will be a big punishment, though.
"The FA and English football will give him more than the Dutch federation gave him because they won't want to be seen as weaker. It will be more than a seven-match ban - I can't believe it will be less. He'll be fined by Liverpool but I think they will stand behind him. Why? Liverpool would be mid-table if it wasn't for Luis Suarez and I think the club is very conscious of that. Without him they are a much weaker side. But for his behaviour Suarez was man-of-the-match yesterday."
Graeme Souness, Liverpool 1978-1984
"The job of directors at a football club is to attract the best players and keep them, but Suarez is making it very difficult for himself to stay at Liverpool and I think [this bite] puts him in the last-chance saloon. Suarez's track record is not great - he had the incident with Evra and this is not the first time he has bitten someone in a football match - but this is embarrassing and puts Liverpool in a bad light in this week of all weeks [the 24th anniversary of the Hillsborough disaster].
"Liverpool are not blessed with world-class footballers and he is genuinely world class, but there are lines you just cannot cross and he has crossed one today - and those pictures will be beamed across the world over the next few days. But the most important thing is to safeguard the good name of Liverpool Football Club as it is world-renowned and up there with Barcelona, Real Madrid and Manchester United. Suarez will suffer but the club will suffer most of all."
Alan Curbishley (former West Ham and Charlton boss)
"It's not a question of if he will be banned, but how long the ban is going to be - and the bigger question is going to be what Liverpool do regarding his future. The statement from Ian Ayre was obviously to try and pre-empt anything from the FA and it was the right thing to do and I thought Brendan Rodgers and Steven Gerrard in their after-match press conferences had been briefed not to talk about it. Later on the statement came out and there were also Suarez's comments, which were trying to pre-empt what is going to happen. For someone who had scored in the 97th minute and had got Liverpool the equaliser, his demeanour as he came off showed he knew that other things were going to come along straight after the game.
"The manager is in a really difficult position here. Obviously Brendan Rodgers doesn't want to lose his talent as a player and I think the fans wouldn't want to lose that, but the decision will have to come from above. Rodgers will be guided by that and the owners will have to have some sort of meeting regarding this and decide where they're going to go. Is he going to be a Liverpool player in the future or is he going to be moved on?"
Alan Mullery, Tottenham 1964-72
"In all my years of playing football and being involved in football, I've never seen an incident like that. I just could not believe what he'd done. It's absolutely outrageous. If it had been me, I would have smacked him straight in the chops. Branislav Ivanovic was absolutely brilliant because he kept calm but if it was me I know where Suarez would have been - he would have been carried off the pitch! The most amazing thing about it is this isn't the first time he's done it! There has got to be something wrong. This fella is an outstanding footballer. Don't get me wrong - you'd love to have him, with his ability, playing in your team. But I tell you what, the things he's got up to are outrageous.
"I've seen players go out for a game with vengeance on their mind because that player has harmed them in the past and gone out and broken their leg. That, for me, was also gruesome and cruel but they could give as much as they took in that era. That was the dark ages. But I could not believe what I was watching yesterday - and whatever fine he has got, it should be doubled and trebled. If I was involved with the football club, I'd want him out of it."