City value the Dutch midfielder, whose contract is set to expire at the end of the season, at around £6.5 million, but Milan are currently willing to pay only £3m-£4m for his signature.
Milan have secured deals to bring strikers Bojan and M'Baye Niang to San Siro and regard De Jong as an ideal replacement for his compatriot Mark van Bommel, who joined PSV Eindhoven.
|13/2||AC Milan are 13/2 with PaddyPower to win Serie A this season|
Milan chief executive Adriano Galliani is considering a variety of bonuses and incentives that could balance a potential offer to De Jong.
A move for Real Madrid midfielder Lassana Diarra, in addition to interest in Kaka, has been abandoned, with the former Arsenal and Chelsea player set to join Fenerbahce for €5.5m [£4.4m] a season for three years.
Djamel Mesbah, Edoardo Pazzagli and Adria Carmona, meanwhile, could leave the Italian club as they look to trim their squad numbers.