City are ready to dangle a new four-year deal, but Milner is fed up being a bit-part player after just 11 Premier League starts last season.
Milner made 31 appearances for City last season, but just 12 starts and at 28-years-old may be hoping to play more of a part at a club.
His lack of game time also hindered his chances of playing for England at the World Cup, with Roy Hodgson only playing him once England’s elimination had been confirmed.
Meanwhile the future of Fabio Borini has been cast back into uncertainty again, despite Liverpool accepting a £14 million bid from Sunderland on Friday.
Speculation on Saturday suggested Borini has turned down the Black Cats’ offer of a permanent move, telling Rodgers he wishes to stay and fight for his place on Merseyside.
However Louise Taylor of The Observer attempts to set the record straight:
While reports that Borini has rejected the transfer out of hand are wide of the mark, Gus Poyet and Sunderland clearly have some persuading to do if they are to sell the idea of a long-term move to Wearside to a player who enjoyed a successful loan stint at the Stadium of Light last season.
The £14m fee would certainly be useful money to Liverpool, especially for a player who cost £10.5m from Roma two years ago.
He has made 20 first-team appearances for Liverpool, scoring twice and started the Reds’ pre-season friendly victory over Preston on Saturday.
The Reds however have already brought in Serbian forward Lazar Markovic this summer, England forward Rickie Lambert and are on verge of completing an £8.5m deal for QPR striker Loic Remy.