The Uruguayan was not involved in Liverpool's 1-0 pre-season defeat to Celtic on Saturday and the Ulsterman says that the striker had a lot of work to do to earn back his place after declaring he wanted an "amicable agrrement" over an Anfield exit.
After two bids from Premier League rivals Arsenal were rejected, Rodgers and chairman John W Henry have remained consistent in their approach that Suarez is not for sale - and the manager says he will only welcome back the player into the first team when he showed his commitment to the club.
"Initially, there will be an apology to his team-mates and the club," Rodgers explained to reporters. "Then, a recognition that he is ready to fight for the club.
"I know that we are not seeing the Luis Suarez I know. He has spent some days working on his own. When he comes back from Uruguay we will see how it goes further.
"We are all on the same page. He won't be going to Arsenal, that's for sure. When Luis is committed to the cause, we will welcome him back with open arms.
"I was made aware at the end of last season that a number of clubs would come in. The reality is that one (club has) done."
Suarez was Liverpool's top scorer in all competitions last season, including 23 goals in the Premier League.
Former Liverpool defender Jamie Carragher revealed on Saturday that he believes Suarez is too good for both Rodgers' side and Arsenal, expressing surprise at the forward's determination to push through a move to the Emirates.