The 26-year-old Uruguayan striker has been at odds with the Reds throughout the summer, going public with his desire to leave after claiming they reneged on a promise to allow him to go if they did not qualify for the Champions League.
Such has been his dissent amid two rejected bids from Arsenal that he has been told to train alone, with manager Brendan Rodgers saying he can only rejoin the first-team squad once he apologises for his actions.
Newspaper reports on Thursday morning also suggested that Arsenal were ready to make a final offer for the striker of £49million.
A lengthy impasse appeared to be on the cards until the El Observador newspaper reported on Wednesday: "For now, owing to all the affection of the people, I would be staying."
Square one appears to have been returned to, though, with Suarez denying making any such statement in the wake of Uruguay's 4-2 win over Japan on Wednesday.
He was quoted by Japan's Kyodo News as saying: "I didn't say that, maybe someone else did and the main thing is that I am here now with the national team."
With that game now out of the way, Suarez is expected to return to Merseyside to address the situation.
He cannot play in Saturday's Premier League opener against Stoke nor any of the following five matches because of a suspension meted out after he bit Chelsea's Branislav Ivanovic last season.
That has not stopped Arsenal chasing him, though, with the Gunners recently bidding £40,000,001 in a bid to trigger a perceived release clause in the former Ajax man's contract.
But Rodgers and Liverpool owner John W Henry have been steadfast in their reluctance to sell their striker, which prompted Suarez to last week take to the media to vent his anger.
In interviews with the Guardian and the Daily Telegraph, 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."