Having picked up the injury on international duty with Spain, Reina missed the 1-0 Premier League home win over Reading on Saturday and will not feature in Thursday's Europa League clash with Anzhi Makhachkala, which is also at Anfield.
The 30-year-old will be keen to be involved in the league trip to local rivals Everton on Sunday, and was quoted on Tuesday as saying he was "getting better, little by little" - although he added that he was prepared to be "patient".
Reina did not take part in the training session with the rest of the Liverpool squad which was open to cameras at Melwood on Wednesday, and when asked how long the keeper was likely to be out of action for, Reds assistant manager Colin Pascoe said: "We are not quite sure at the moment.
"Hopefully not too long. He is doing his rehab at the moment and is working hard in training.
"So we will just have to assess him over the weekend and we will see then."
Brad Jones deputised for Reina in the Reading game and is set to do so again for the Anzhi contest.