Wolves' Bakary Sako has revealed he is mulling over offers from the Premier League but is yet to decide on his future.
Rotherham boss Steve Evans will decide the fate of his out-of-contract players in a meeting on Monday.
Striker Suarez had been linked with a move to Juventus, with the Italian giants reportedly planning a double swoop on the Barclays Premier League by also poaching Arsenal's Robin van Persie.
But despite occasionally troubled times on Merseyside, the Uruguay international has given new Reds manager Brendan Rodgers a boost ahead of the new season by committing himself to the Reds cause.Suarez, back in training at Melwood on Tuesday following his recent involvement in Uruguay's failed bid for Olympic gold, has confirmed he could not be more content with life on Merseyside.
"To sign a new contract with Liverpool is unbelievable for me because I am so happy here at both the club and also in the city," Suarez told Liverpoolfc.com.
"That is important for me and I am very happy with my new contract.
"When you are a kid, everybody wants to play for Liverpool. I am here now and it is a dream for me, and now I am a Liverpool fan.
"I am happy off the pitch because the people of Liverpool are good with me and my family.
"I try my best on the pitch and when you are happy off the pitch, you are happy on the pitch.
"I want to say thank you to the fans because they are our 12th player. The supporters of Liverpool are unbelievable.
"Five or six years ago I watched on TV the stadium and the club, and now I play here and the supporters have helped me. That's very important for me."
Liverpool accidentally broke the news on their television channel earlier in the day before the report was swiftly pulled, citing a 'temporary fault'.
A short announcement confirmed Suarez, who has scored 21 goals in 52 matches for Liverpool, had put pen to paper on the deal on Tuesday.
It was not until another four hours later, at 6pm BST, the club finally confirmed Suarez had pledged his future to the Reds.
Despite the gaffe, Rodgers is naturally delighted to be working with a player of Suarez's calibre.
"When you have the opportunity to work with world-class players it's fantastic," said Rodgers.
"There were certainly a few clubs who were interested in him, but over the off-season he and I communicated well and he's committed himself for the long term here now.
"He's really looking forward to playing in this way of working.
"As a manager and for the supporters, I'm delighted because I know how important he is for them."
It has not all been plain sailing for Suarez, though, as it was in October last year his troubles began after Manchester United defender Patrice Evra made an allegation the 25-year-old had racially abused him during a 1-1 draw at Anfield.
The high-profile incident resulted in the Football Association banning Suarez for eight matches and fining him £40,000.
Fuel was then added to the fire when, on his return to the first team for the clash with United at Old Trafford, Suarez refused to shake Evra's hand prior to scoring in a 2-1 defeat.
It resulted in United manager Sir Alex Ferguson branding Suarez "a disgrace to Liverpool Football Club", further adding he "would get rid of him if I were them".
Suarez issued an apology the following day and went on to finish the season with a flourish, scoring nine goals in 17 matches.