The Mirror says City have stepped up their bid for Milner by telling Aston Villa in face-to-face talks of their determination to sign the England ace.
Mega-rich City had an initial bid of £18million plus £2m in add-ons rejected by Villa last month.
But City are willing to return with another offer for the versatile midfielder as soon as England's World Cup campaign is over.
City chief executive Garry Cook sought out his Villa opposite number Paul Faulkner at the Premier League gathering earlier this month.
The two-day meeting of all Premier League clubs took place on June 3 and 4 at Stapleford Park in the Midlands.
And Cook and Faulkner had private talks at the four star country house hotel after a group meeting with fellow club chiefs.
Villa do not want to sell Milner but are resigned to cashing in if he fails to sign a new long-term contract.
They are refusing to put a price tag on the 24-year-old, but City hope to get their man with an offer of between £27-30m later this summer.