City believe Everton will sell the England international for £45 to 46 million.
Stones has been heavily linked with a move to the Etihad Stadium this summer, with Blues manager Pep Guardiola thought to view him as the ideal addition for his defence.
They have failed to agree a deal for him as yet, with Everton slapping a £50 million price tag on his head.
Everton remain firm on their asking price, although the feeling at the Eithad is that they will ultimately settle for a fee of around £45 or £46 million.
Guardiola is willing to offer Wilfried Bony as a makeweight in the deal but the Toffees want a straight cash deal.
It now remains to be seen if the two clubs can agree a fee, with Everton unlikely to move on their asking price despite City’s belief to the contrary.
Everton will be keen to get this transfer saga finished sooner rather than later though, with the move likely to play a big role in their own transfer dealings this summer.