Both giants have been encouraged by Ruiz stalling over new contract negotiations with the Azzurri. It's understood Ruiz is unhappy with Napoli's attempts to insert a €180m buyout clause.
La Repubblica says City and Real are both planning to move for the Spain international this summer, with the Sky Blues viewing him as a replacement for the departing David Silva.
For his part, Real president Florentino Perez has already seen enough and plans to make an €80m offer for Ruiz in the coming weeks.
However, Napoli are seeking at least €100m to part with their young midfield schemer.