England midfielder Delph's £8m move to City appeared over after he released a statement to "set the record straight" over his future, but Delph, 25, appears to have had another change of mind.
He was scheduled for a medical seven days ago after City agreed to meet an £8m release clause.
That was inserted into the player's new four-and-a-half-year contract signed in January.
Delph released a statement last week after reports of his original medical at City, saying: "I'm not leaving, I'm staying at the football club."
The former Leeds player, who did not travel with the Villa squad for their pre-season training camp in Portugal, is now set to complete a second U-turn.
City are in Australia where they are preparing for the new Premier League season with a number of games.
