The 22-year-old has been absent for the Reds since September, when he ruptured the anterior cruciate ligament in his right knee.
"I've been taking my time with this injury and making sure that I'm spot on with all parts of the rehab," Kelly told the official website.
"This is not an injury that you can mess about with, so I've been taking it steadily. We're hitting all the targets and I should be fit before the end of the season."
Kelly recently penned a new long-term deal at Anfield.