The 29-year-old Republic of Ireland international is now negotiating with Villa over personal terms.
Dunne's future at Eastlands looked uncertain following the arrival of Joleon Lescott from Everton this week.
Dunne was in the team that defeated newly-promoted Wolves last weekend but that looks likely to have been his final match for City.
Club captain Dunne joined City from Everton for £3 million in October 2000.
It was Stuart Pearce who handed him the captain's armband at the start of the 2006/07 season.
Dunne was on the pitch for every minute of every game that season, both league and cup, and went on to land fans' player-of-the-season honours for the third successive time. Twelve months later, he made history by picking up the coveted award for the fourth time.
The big defender continued as City captain under Sven-Goran Eriksson and Mark Hughes and is still a vital member of the Republic of Ireland team.