Sturridge missed Liverpool's 2-0 Premier League win over Newcastle United on Monday after injuring his hip during last week's 1-0 quarter-final replay win at Blackburn Rovers.
But the England international striker could return on Sunday as Liverpool bid to reach their first FA Cup final since 20011-12.
"Daniel Sturridge was injured from the Blackburn game and he just wasn't right for tonight. It's his hip but hopefully he'll be okay for the weekend," Rodgers told reporters on Monday.
"I'll probably know more in the week. He said he feels reasonably fine, so we're hoping by the middle of the week we'll have a good indication of where he's at."
One player who will definitely miss Liverpool's trip to Wembley is France international defender Mamadou Sakho.
Sakho has been nursing a hamstring issue and is facing "three to four weeks" on the sidelines, according to Rodgers.
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
