The Spain back-up keeper, 30, did not play in the 1-1 draw with France but “felt a slight twinge at half-time” according to Reds boss Brendan Rodgers, and will undergo a fitness test on Friday to see if he can line up against the Royals.
“We'll wait another 24 hours to see how he is,” Rodgers said. “It's nothing overly serious - he felt just a slight twinge in his hamstring at half-time in the game.
"We had the checks on him and he had a scan this morning. It's not overly-serious, but we just need to weigh up the risk in the next 24-48 hours.
"I think Spain picked up a few injuries. By all accounts the pitch wasn't the best and a number of them picked up muscle injuries.”
Rodgers confirmed that, if Reina has not fully recovered, Australian Brad Jones will start in his place.
"It's good for us that if he can't play, we've got Brad Jones, who has made fantastic improvement since the beginning of the season and shows up every day of his life very well here,” Rodgers added.
"So if Pepe can't play, we've got an able understudy who can come in and do very well, I'm sure."
Rodgers said that he had no other major worries following the international break, although Uruguay duo Luis Suarez and Sebastian Coates are yet to return from Bolivia and will return later on Thursday.
Suso, meanwhile, will sign a new improved deal at the weekend.
The Spain U19 international forward, who is just 18, is expected to be a first-team regular following the foot injury that ruled Fabio Borini out for three months.