The Spaniard has been struggling with the problem for some time and has featured just twice in the Reds' last five matches, with one of those appearances a 30-minute substitute appearance.
"Jose Enrique has been struggling for a little while with an injury," manager Brendan Rodgers told talkSPORT.
"He will probably need an operation. It's a blow for us because he's a very talented player."
The 27-year-old full-back, who has only made six Premier League starts this season, had come in for some criticism for his performances this season.
Meanwhile, Sky sources understand that the club's Head of Coaching Rodolfo Borrell and Academy Director Frank McParland and have both left their posts.
Borrell was brought to the club by former manager Rafa Benitez in 2009, having previously spent 13 years working with Barcelona where he helped develop the likes of Lionel Messi, Gerard Pique and Cesc Fabregas.
McParland also joined the club in 2009 and has overseen the development of Andre Wisdom, Raheem Sterling and Martin Kelly all of whom have broken into the first team set-up at Anfield.