The Northern Irishman demanded that the Uruguay international apologised for his recent conduct, where he claimed that the Merseyside club have gone back on their promise to let him leave Anfield for a Champions League outfit this summer.
While there have been reports that Suarez is not prepared to say sorry, Rodgers has reiterated that he wants an 'amicable' resolution to the situation.
"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," Rodgers told the club's official website. "If you don't have that commitment, and those standards, then you won't play. It's as simple as that.
"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'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% commitment, then there will be no solution."
Arsenal are said to currently be the only club interested in signing Suarez following two rejected bids.