Delph pleasantly surprised Villa fans by agreeing fresh terms in January, six months before his deal ran out.
City are keen to add more homegrown talent to their squad after the loss of James Milner.
Losing Delph would be a huge blow to Tim Sherwood, who made the 25-year-old his captain after taking over.
The Villa manager is already on the lookout for central midfield recruits after Tom Cleverley opted to join Everton.
Charlton’s Jordan Cousins and Hull’s Robbie Brady are both targets for Sherwood.
Original source: Delph could join City for only £8m