The Wolves midfielder has impressed so far in the Premier League this season, earning plaudits from the media and other clubs.
City manager Pep Guardiola wants to add strength to his midfield, after missing out on Jorginho to Chelsea in summer, while Mourinho, as reported by 'The Sun', is willing to fight his rivals for the player's signature.
Fernandinho is Guardiola's only option in defensive midfield, and with the Brazilian having turned 33 in May, it is unlikely he has the legs to start every game this season.
Mourinho, however, shares the same agent - Jorge Mendes - as the 21-year-old, which could be a decisive factor in a move for Neves.
The two Manchester sides have also battled for the signatures of Alexis Sanchez and Fred in previous windows, with the 'Red Devils' coming out on top.