Rodgers said Suarez, who was seeking a move away from the Merseyside club during the off season, will need to mend relations when he returns from playing for Uruguay in a friendly in Japan on Wednesday.
"Initially there will be an apology to his team mates and the club, then a recognition that he is ready to fight for the club," Rodgers told reporters after Liverpool had lost to Celtic in their final pre-season friendly in Dublin on Saturday.
"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 (international duty with) Uruguay we will see how it goes further," he added.
"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."
Liverpool turned down a 40 million pound offer from Premier League rivals Arsenal after Suarez sought to extricate himself from his contract on the basis that the club had failed to qualify for the Champions League this season.
"I was made aware at the end of last season that a number of clubs would come in. The reality is that one have done," said Rodgers.
Rodgers ordered Suarez to train alone after the 26-year-old told Spanish sports daily Marca in midweek he wanted an "amicable agreement" to leave Liverpool and thought a bid over 40 million pounds was enough to trigger a clause in his contract.
Suarez, who scored 29 goals in all competitions for Liverpool last season, received full backing from the club and the solidarity of fans during two controversial incidents that have marred his two and a half years at Liverpool - a racist outburst at Manchester United's Patrice Evra and biting Chelsea's Branislav Ivanovic.
(Reporting by Rex Gowar, editing by Pritha Sarkar)
