It has been claimed for some time that City are one of a number of clubs interested in signing the Netherlands international, and it appeared that their chances had increased when Liverpool pulled out of the race.
However, with Southampton keen to keep the player, they have set his asking price at £70m and according to the Manchester Evening News, City have decided to rule out the possibility of going above their own valuation.
It has been suggested that City are open to spending above £50m for Van Dijk, but they will not entertain the idea of raising that to £60m.
Their stance appears to leave Chelsea as the frontrunners for the 25-year-old, but they, too, may baulk at going as high as £70m.
Since the Saints paid £11.5m for his signature in September 2015, Van Dijk has made 55 appearances in the Premier League.