Striker Borini needed surgery after dislocating his shoulder against Swansea in February, while defender Kelly has been sidelined since September with a cruciate ligament problem.
Anfield's head of performance, Glen Driscoll, said both players had a chance of returning before the end of the season but admitted to caution over Kelly's comeback.
"Martin is doing extremely well; he's probably at the late stage of his rehab," Driscoll told Liverpool's official website.
"We'll probably look to prioritise getting him back for pre-season 110 per cent fit - 10 per cent fitter, stronger and quicker, more powerful and agile than he was previously.
"He'll probably be in a position where it will be tempting to put him into games again this season. But we want to make sure that he's in a very strong position so he can fly next season.
"Martin has almost been a showcase for the quality of our medical science department. He's getting the best of all our staff and it's going very well."
Borini has suffered two long-term absences from the first team this season, but Driscoll believes the forward could return before the campaign concludes.
He added: "Fabio Borini was outside for the first time (on Friday), so he's starting that progression - passing balls, running and doing ball work. He's due to be probably another six weeks from this point on.
"The injury he's had is normally eight to 12 weeks. He's quite a quick rehabilitator.
"At the moment, it's looking pretty positive for Fabio that he could be back ahead of schedule and maybe make the end of the season."