Press Association Sport understands Villa had been expecting a bid for the 25-year-old, who did not travel to the club's training camp in Portugal on Thursday, all week.
It seems City have now triggered an £8million release clause included when Delph signed a new four-and-half-year deal in January.
City are keen to boost their home-grown quota following the loss of James Milner to Liverpool and Frank Lampard to New York City and Delph has been on Manuel Pellegrini's radar for some time.
The squad are currently in Australia for the start of their pre-season preparations and Delph is expected to join them once the formalities on his deal have been completed.
They are also monitoring the situation with Liverpool's Raheem Sterling, who returned to training on Friday after two days' absence with illness.
City have had two bids rejected, the last an offer of £40million, but are reluctant to meet the Reds' £50million valuation.
As it stands Liverpool expect Sterling to be on the squad's flight to Thailand on Sunday for their pre-season tour.
Source : PA
Source: PA