Jurgen Klopp has spent the 2017-18 campaign rotating his options between the sticks, with Loris Karius currently being favoured to Simon Mignolet.
Nicol is not convinced by either and believes the Reds need to be in the market for a new No. 1 this summer.
The former Reds star told ESPN FC: “To be honest I think Liverpool should go and see if they can either get a No. 1 or have somebody who’s on a level with Karius.
“Mignolet isn’t, he’s clearly the No 2 and I think what Mignolet’s doing is waiting to see if he can get a game in the World Cup.
“[Thibaut] Courtois has had a couple of injury nicks recently and a good World Cup would mean Mignolet is in the shop window and he could get himself a good move.”
Liverpool spent big in January plugging a defensive hole with £75 million centre-half Virgil van Dijk, and Nicol feels they should be looking to Italy for another long-term solution in a problematic position.
The Scot added: “Liverpool’s problems were always the defensive unit and by that, more importantly, the centre-back position and the goalkeeper.
“They’ve certainly made a difference signing Van Dijk in the centre-back position.
“Karius, as good as the last couple of months he has had, are we really 100 per cent relying on him? I’m not ready for that yet.
“That means Liverpool, in my opinion, have to go out and get a recognised No 1.
“I would have no problem with him [Roma keeper Alisson], I would have no problem if they can get the likes of Donnarumma who would be a goalkeeper for the next decade.
“But I think definitely it’s a priority now for Liverpool. It is a weak spot, again as good as Karius has been recently, he’s not the finished article by a long way.”