The 30-year-old, who missed last Saturday's 1-0 win over Reading in the Barclays Premier League, will be keen to be involved in the 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 morning, and asked on Wednesday afternoon 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.
The Reds will also be without sidelined trio Martin Kelly (knee), Lucas Leiva (thigh) and Fabio Borini (foot).
Liverpool (from): Jones, Gulacsi, Johnson, Enrique, Agger, Coates, Wilson, Carragher, Coady, Skrtel, Flanagan, Wisdom, Robinson, Sahin, Gerrard, Cole, Henderson, Downing, Allen, Sterling, Shelvey, Suarez, Assaidi, Pacheco, Suso, Yesil, Morgan.