They also have been given the impression by the Italian champions that they don’t want to sell Pogba, 22, in this transfer window, having already seen Carlos Tevez and Arturo Vidal depart from Turin.
So City are prepared to wait, either until January or even next summer.
Juventus have also knocked back a £60m bid from Barcelona for Pogba.
City, though, are continuing the £50m pursuit of Wolfsburg winger Kevin De Bruyne, 24.
Meanwhile, Man City centre-half Eliaquim Mangala and Liverpool defender Mamadou Sakho have been backed to come good this season.
The French duo arrived in the Premier League with big reputations – Mangala cost City £32m and the Reds spent £18m on Sakho – but they have struggled to convince.
But ex-France boss Raymond Domenech believes they are both now ready to prove themselves.
He said: “Mangala must be better in the second year.
“He made some mistakes, so he has to correct his mistakes."