Jurgen Klopp preferred the 22-year-old goalkeeper over Adrian against Ajax on Tuesday night after Alisson picked up an injury.
And the shot-stopper did not disappoint as he made some fine saves to make sure Liverpool earned three points from a game they won 1-0 at Anfield.
Nicol is keen to wait until the weekend to see whether Kelleher has replaced Adrian as the second choice goalkeeper at Liverpool.
However, he sees no reason why Adrian should not be demoted to being the third-choice goalkeeper at Liverpool as he thinks the Irishman looked more assured and is the future of the club.
The former defender stressed that it is time for Kelleher to replace Adrian as the number 2 at Anfield.
Nicol said on ESPN FC: “I think that’s probably the right thing to do, I guess we will find out at the weekend if Alisson is still injured, which he probably will be, where he is actually down to three.
“I would suggest that on the back of a great performance from Kelleher against Ajax, you need to look to the future.
“And right now he is the future and so I think you can trust him, certainly you can trust him more than you can trust Adrian.
“Honestly for a young lad who has made just two first-team appearances, one in the League Cup, one in the FA Cup, he looked really calm and really solid, which is pretty much the opposite of what Adrian been.
“I think now is the time.”
It remains to be seen whether Alisson will be fit to take his place between the sticks when Liverpool host Wolves on Sunday.
