The Uruguayan striker - the subject of two failed Arsenal bids - has been forced to train alone since claiming Liverpool reneged on a promise to let him leave this summer for a Champions League club.
Manager Brendan Rodgers subsequently accused Suarez of showing "total disrespect" and, speaking after a pre-season defeat to Celtic, said only after an apology would he be welcomed back into the Anfield fold.
But it is understood the forward currently feels has he no reason to oblige and believes his behaviour has in no way shown disrespect to a club determined to keep him.
"Initially there will be a recognition that (there needs to be) an apology to his team-mates and the club," Rodgers had said on Saturday.
"I have seen him over a period of time. I know it is not the Luis Suarez we know and I have to protect the fans and the players because they deserve more than that."
Both Rodgers and Reds owner John W Henry have dismissed their star forward's claim of broken promises.
Suarez is prepared to take the issue to the Premier League to force his exit but Liverpool insist they do not have to sell and believe Arsenal's bid of just over £40m is well short of his value.