The 23-year-old has spent a lengthy time on the sidelines after damaging his anterior cruciate ligament in the Reds' 2-1 defeat to Manchester United at Anfield last season.
"I'm feeling a lot sharper," Kelly told the Liverpool Echo. "I've been doing some additional training over the past few weeks and I'm ready to push on.
"It has taken longer than I hoped to get back to this level but that's been brought on by us not being in the Europa League or having much of a run in the League Cup. It's been difficult to get game time as the manager has to pick his best XI to start every game."
Kelly made his third substitute appearance of the season in Liverpool's 4-1 win over West Ham United last weekend.