La Gazzetta dello Sport says City and Barcelona are interested in the Holland international.
For the first two weeks of July, Dumfries can leave Inter for a set fee of €30m thanks to a clause in his current contract.
And he has been in contact with super agent Jorge Mendes, with the hope of setting up a move to City.
Dumfries, despite the interest of Barca, favours joining City, particularly given the chance to work with manager Pep Guardiola.