The England midfielder will join the club on July 1, subject to a medical, after his contract at the 2013/14 Premier League champions expires.
And the Sky Sports pundit says Milner could now rival Jordan Henderson both for his position in Brendan Rodgers’ midfield and also as a potential successor to Steven Gerrard as club captain.
“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 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 has won two Premier League titles, the FA Cup and the League Cup since joining Manchester City from Aston Villa in 2010.
But after he started just 18 Premier League matches last season, Carragher applauded the 29-year-old for his willingness to move to a team that isn’t playing in the Champions League.
He added: “I think it’s a very good signing – a free transfer who can play in a few positions and has great experience.
“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.”