Reports emerged yesterday that Manchester United are hoping to hijack the Reds' interest in the 29-year-old.
It was thought United's transfer negotiator Ed Woodward has made enquiries for Milner.
The England international, who is a free agent this summer, has yet to sign a new deal with the Citizens despite being offered a £130,000-a-week contract.
However, fresh reports indicate Arsenal and Liverpool have both held talks with the player, who is expected to decide his future after England's upcoming games against the Republic of Ireland and Slovenia.
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James Milner is a free agent this summer
Milner made 32 Premier League appearances for the Citizens last season.
But he is believed to want to play in a more central role.
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