The Serbian picked up a tendon injury during the Reds' participation in the International Champions Cup but boss Rodgers expects to have him back in the coming weeks.
Lazar Markovic could hand Liverpool a timely boost ahead of Sunday's Premier League opener with Southampton by returning to full fitness.
The offseason signing from Benfica has missed the final four games of Liverpool's preseason schedule with a tendon problem sustained on his debut against Olympiakos in Chicago.
However, Brendan Rodgers is optimistic that the winger could be available for selection against Southampton. And, if Markovic does miss out, the Reds boss expects to have him at his disposal when last season's runner up travels to champion Manchester City the following week.
"He'll hopefully be around then [for the Southampton match], but if not then he certainly will for the next game," Rodgers said after Liverpool thrashed Borussia Dortmund 4-0 on Sunday. "He had a slight problem with his tendon, but he's up to speed.
"He's working with our sports science team. He's looking very strong and if he just misses out, he certainly should be available for the next game."
Markovic made 49 appearances in all competitions for Benfica last season and scored seven goals, before he was snapped up by the Merseyside outfit for 20 million pounds this summer.