Aldridge can't see Kelleher staying with Giorgi Mamardashvili to arrive from Valencia next summer.
He wrote for the Sunday World: "I’d say he would get into pretty much every other Premier League team as first-choice keeper and I include Manchester United, Tottenham, Chelsea and most teams in the top half of the table in that list of top-flight sides.
"So, while there were suggestions last summer that Kelleher might move to a club in the Championship after confirming he had asked to leave Liverpool in the hunt for first-team football, he’s far too good for that.
"He should be playing every week in the Premier League and with his 26th birthday coming up next month, he will need to leave this summer to make that happen.
"The club has signed Giorgi Mamardashvili for next season and the big Georgian has not signed to be a No 2. That suggests the club view him as the successor to Alisson.
"That signing was a kick in the teeth for Kelleher and you wonder whether Liverpool will regret letting him go because he has proved he can handle the pressure when it matters. He is definitely up to the job."