The 29-year-old Manchester City midfielder, whose contract expires at the end of next month, is in advanced talks over a free transfer to the Reds.
Milner has won two Premier League titles with his current club, played in the Champions League and made 53 appearances for England, and Carragher thinks if he does complete a move he will rival current vice-captain Jordan Henderson as the successor to Steven Gerrard, who is joining the Los Angeles Galaxy this summer.
"Brendan Rodgers will have spoken to him about where he sees him fitting in but he's very similar to Jordan Henderson," Carragher wrote on sports social network Kicca.
"I have no doubt one reason he's joining is to play in a more central role rather than out wide.
"Could Milner play a holding role? Maybe, but I don't think that's what suits him.
"His main strength is his engine, which could suit him and Jordan to both play alongside a holding midfielder (Emre Can?) but his best position is tucked in from the right in a central role which is also Jordan Henderson's so it'll be interesting how those two fit into next year's midfield set-up.
"The fact that Brendan Rodgers wouldn't confirm Jordan Henderson as this season's captain even though he was captain in Gerrard's absence last season makes me think him and Milner could be competing for the armband.
"Was that another thing that enticed Milner to join?"
Milner had been consistently selected by the likes of Roberto Mancini and Manuel Pellegrini for his current club and Fabio Capello and Roy Hodgson at international level.
However, with first-team opportunities starting to dwindle at the Etihad Stadium - he made just 18 league starts last term - Milner is seeking a new challenge and Anfield now appears his likely destination.
The completion of a deal may not be ratified until July 1 as the player is still under contract, but could come as early as the end of the week, and Milner is likely to be the first one of Rodgers' signings through the door this summer.
"I think it's a very good signing - a free transfer who can play in a few positions and got great experience," Carragher added.
"A good character, which you can see from the fact he's left Man City in the Champions League for Liverpool.
"That shows regular starts mean more to him at this time than being a squad player with more chance of picking up trophies at City."