Rodgers said the Uruguayan would have to show contrition in order to return to the first-team fold after Suárez claimed his coach had reneged on a pledge to let him leave for a Champions League side.
Liverpool would not confirm how - or even whether - an apology had been made ahead of their Premier League season opener with Stoke on Saturday.
Suárez is suspended for the opening six domestic matches of the campaign as he serves out his 10-match ban for biting Branislav Ivanović.
Arsenal have had two bids for the player rejected, including one of £40,000,001 in an attempt to activate a clause in the 26-year-old's contract.
After last weekend's friendly defeat to Celtic in Dublin, Rodgers confirmed Suárez would need to say sorry before any reintegration took place.
"Initially there will be a recognition that (there needs to be) an apology to his team-mates and the club," he said.
"When he is back from his international trip (Suarez went to Japan with Uruguay in midweek) we will assess it from there.
"He is a world-class striker and when he is committed to the cause we will welcome him back with open arms.Suggest a correction