Manchester City had a £20m bid for Milner, who joined Villa in a £12m deal from Newcastle in 2008, rejected earlier this summer.
Following that, O'Neill revealed that Milner "intimated he wanted to go" but added that the club will not allow the player to leave unless their valuation is met.
"City made an offer but it did not meet our valuation. I'd imagine things will be resolved in the foreseeable future," said the Northern Irishman last week.
The ongoing transfer saga echoes that which resulted in Gareth Barry eventually swapping Villa Park for Eastlands in June 2009 in a £12m deal.
And BBC Sport's football reporter Pat Murphy said on Radio 5 live: "O'Neill wanted to talk to Milner over his version of a meeting held on 31 May attended by, amongst others, owner/chairman Randy Lerner.
Unless Milner makes it clear he wants no part in Villa's future, he will have to travel with the squad to Portugal on Wednesday for pre-season training
BBC Sport's football reporter Pat Murphy
"O'Neill is adamant Milner would not discuss a new contract. As far as O'Neill is concerned, Milner wanted to leave Villa.
"Milner, however, is challenging that interpretation - possibly because the player fears a backlash from supporters similar to that experienced by Barry a couple of years ago. But O'Neill is in no mood to have his version of that 31 May meeting challenged.
"Unless Milner makes it clear he wants no part in Villa's future, he will have to travel with the squad to Portugal on Wednesday for pre-season training."
Manchester City have splashed out more than £80m this summer already, prompting many to tip Roberto Mancini's outfit for a Premier League title challenge this season.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.