The striker has been at loggerheads with his club all summer, having claimed that his employers had reneged on a deal to allow him to leave should they fail to qualify for the Champions League.
Arsenal have tried to sign him twice, bidding £40,000,001 in an attempt to activate a release clause that Suarez claims is in his contract.
The Uruguayan has been forced to train alone by Reds manager Brendan Rodgers, who has said the player can alone return to the first-team squad once he apologises to his team-mates.
That impasse looked likely to move Suarez to the exit door, but Suarez appeared to backtrack today, telling Uruguayan newspaper El Observador as saying he is willing to remain at Anfield because of the supporters.
Suarez, who is banned for the first six games of the coming season for biting Chelsea’s Branislav Ivanovic, was quoted as saying: “For now, owing to all the affection of the people, I would be staying.”
The newspaper adds that the 26-year-old may now pen a new deal with Liverpool.
Such a development would be a major coup for Liverpool, who had long maintained that they would not sell the player to a rival English club.
Arsenal, too, would be left in a difficult situation, having failed to attract a big name to the club despite bold claims by chief executive Ivan Gazidis at the start of the summer that the club now had the funds to compete with their rivals in the transfer market.
The transfer window does not shut until September 2 and, given the number of twists and turns in the Suarez saga, it is conceivable that he could still depart.
Only a week ago he gave interviews to the Guardian and the Daily Telegraph in which he suggested he had been betrayed by Liverpool.
He 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.”