The 25-year-old has been Liverpool's second-choice stopper for several seasons, with his appearances largely restricted to the cup competitions.
Since making his debut in the 2019/20 campaign, the Cork-born goalkeeper has only made 27 first-team outings for the Reds in all competitions – just five of which have come in the Premier League.
However, Kelleher has largely impressed when called upon, most notably in penalty shootout situations. The Republic of Ireland international has won for shootouts for the Reds and even scored the winning spot kick in the League Cup final win over Chelsea.
Speaking ahead of the Europa League tie with LASK on Thursday, Klopp called on Kelleher to use the opportunity he has now been given by Alisson's unfortunate injury.
"He would have played anyway," Klopp said in reference to Thursday's game. "Nobody, Caoimhin included, wanted Ali to get injured, but if these kinds of things happen you need the strongest possible option. That's Caoimhin for us. He deserves his opportunity to get a few more games and hopefully show his full potential."
Kelleher is likely to get a run of at least the next five games in goal for the Reds – three of which come in the Premier League – with Klopp suggesting that Alisson should be on track to return in time for the clash against Manchester United on 17 December.
He said: "With Ali, it's a bit lesser [than Jota's injury], so we have to see - not day by day, he will not play tomorrow, not on Sunday, probably not the week after. Then it should be kind of okay."
Following the home game against LASK, Liverpool take on Fulham on Sunday (3 Dec), before clashes away at Sheffield United (6 Dec), Crystal Palace (9 Dec) and Union Saint-Gilloise (14 Dec).