Suarez has made it clear he wants to leave to play Champions League football - a move he insists Liverpool had agreed to allow if they did not qualify for the competition themselves.
Arsenal is the current destination of choice after they lodged a bid of £40million plus £1 - a figure they think triggers a clause in the Uruguayan's contract - but the Reds are standing firm over their position that the striker is not for sale.
Last season's current top-scorer has been made to train alone by Rodgers until he apologises publicly and privately for his recent conduct, a move he is highly unlikely to make according to reports today.
Rodgers reiterated that he would not soften his stance on Suarez until the club could be guaranteed his undivided commitment, but did suggest the relationship was not beyond repair.
"It is something that we have to do everything we can to fix," Rodgers told the club's official website.
"If we have got to sit and wait, then so be it. But this is a club that has got great values, and we hope that the situation can be resolved amicably, and I am sure it will be.
"There has been a lot said and a lot reported, and we have made a stance, as a club and as a manager, of the commitment and the standards required.
"If you don't have that commitment and those standards then you won't play. It's as simple as that.
"There's no problem between me and him, it is quite calm. But obviously I have got to respect the club and the team.
"It doesn't matter who you are, if they're not pulling their weight then they are letting down the club, the city and everyone who has stood by them.
"So until I get that assurance that we are going to get nothing but 100 per cent commitment, then there will be no solution."
Former Liverpool defender Jamie Carragher, who retired in the summer after spending his entire career at Anfield, thinks the club's owner John W Henry risks looking "stupid" if Suarez moves on.
Henry has told Arsenal to give up on the move in no uncertain terms, a fact which Carragher feels bolsters Liverpool's resolve on the matter.
"I expect him to stay at Liverpool now," Carragher told the Daily Telegraph.
"I think if you come out as owner and say that, and then something happens, you make yourself look stupid. I'm glad he has done it and I think everyone in football should be glad he has done it. It is maybe a message for players."
Carragher, 35, admitted that he had noticed a change in his former team-mate when he made a brief return to the training ground ahead of Steven Gerrard's testimonial.
He said: "I've only seen him once. God knows what he has been like all pre-season, but he hasn't been his normal self."