The striker has been at odds with his club all summer over his future, last week saying Liverpool had reneged on a deal to allow him to leave should they fail to qualify for the Champions League.
Arsenal have tried to lure him away as a result, bidding £40,000,001 in an attempt to activate a clause Suarez claims is in his contract, and Liverpool manager Brendan Rodgers has ordered his player, who has been training alone, to apologise to his team-mates before he can return to the first-team squad.
But Suarez, who is banned for the first six games of the season after biting Chelsea's Branislav Ivanovic, is currently away with Uruguay for their friendly in Japan.
And he has been quoted in Uruguayan newspaper El Observador as saying he is willing to remain at Anfield because of the supporters.
"For now, owing to all the affection of the people, I would be staying," he said.
The newspaper goes on to suggest the 26-year-old may even sign a new deal with Liverpool, which would represent a remarkable turnaround from a week ago.
Then, in interviews with the Guardian and the Daily Telegraph, Suarez said: "Last year I had the opportunity to move to a big European club and I stayed on the understanding that if we failed to qualify for the Champions League the following season I'd be allowed to go.
"I gave absolutely everything last season but it was not enough to give us a top-four finish - now all I want is for Liverpool to honour our agreement.
"I don't feel betrayed (by Liverpool) but the club promised me something a year ago just as I promised them that I would stay and try everything possible to get us into the Champions League.
"They gave me their word a year ago and now I want them to honour that. And it is not just something verbal with the coach but something that is written in the contract. I'm not going to another club to hurt Liverpool."
Rodgers and principal owner John W Henry have been steadfast in their stance that Suarez will not be sold, but the player had said he would be willing to go to Premier League arbitration in order to secure a move away.
Suarez added last week: "I have the club's word and we have the written contract and we are happy to take this to the Premier League for them to decide the case but I do not want it to come to that. We have the backing of the PFA."
Liverpool's fans have remained loyal to Suarez throughout a number of controversial issues over recent seasons, including his biting of Ivanovic and his use of racist language to Manchester United's Patrice Evra.
Even this summer they have warmly applauded him, first at Steven Gerrard's testimonial game last weekend and then at an open training session last week.
If Suarez stands by today's quote, though, it would appear their backing has had an impact and, if he obeys Rodgers' orders, he could be back in the first-team picture when his suspension ends.
"Initially there will be a recognition that (there needs to be) an apology to his team-mates and the club," Rodgers said at the weekend.