The Spaniard has been left out of Brendan Rodgers' starting XI in recent weeks and was criticised by his manager, who warned that he could be sold after raising questions over his attitude and desire to play for the club.
Enrique is thought to have picked up the injury prior to the Reds' first game of the season against West Brom and, despite struggling through the last two months, the 26-year-old is hopeful that an injection will allow him to play pain free and prove his worth to Rodgers.
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"I don't know quite what the problem is but I have been playing with a lot of pain," he told the club's official website.
"I had an injection in my knee so hopefully that will settle it down and allow me to find my form again because it is difficult playing with pain.
"It is something behind my knee and I have had to be very careful with it. I've been trying to play with it but it is not 100 per cent.
"I felt it in training before the opening day of the season at West Brom and since then it has been very bad. Hopefully the injection will sort it out.
"Obviously with a new manager at the club you want to be at your best, but I want to play to help us climb up the table. I want to get back as soon as possible."