The problem forced the Spaniard to miss today's 5-0 win over Norwich City at Anfield, although at the time no reason had been given for his absence.
"He had a thigh problem before the game last week. He played and on assessment afterwards it got worse. Plus he broke his nose [in the game]," Rodgers told reporters.
"He had an operation to fix his nose yesterday. We'll see how he is by next week and review it from there."
Reina has made 24 appearances in all competitions this season.