The England international has had an injury-disrupted season, making just seven Premier League starts so far.
After playing 85 minutes as Liverpool picked up a 1-0 win at Blackburn Rovers in their quarter-final replay on April 8, Sturridge was forced to sit out Monday's league win against Newcastle United with a hip problem.
Sturridge was reported to have missed training with the issue on Thursday, but Rodgers has not given up hope of fielding the forward at Wembley.
"We will give him every possibility to be fit for the game," said Rodgers.
Liverpool are looking to win the FA Cup for the first time since 2006.
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