The defender, who impressed on his debut against Lyon, is hoping to make his second start for the first eleven when the Reds take on Lille in the Europa League tonight.
"The ankle feels fine now and it's good to be fit again and train without any problems," said Kelly.
"Hopefully the injury is behind me now and I can push on.
"I was pleased with my performance against Lyon and thought I did well, so hopefully I can push on and play more games and prove myself.
"The injury came at a bad time for me because I could have got more chances, but that's football and you've got to get over your injuries and come back stronger."