Keisuke Honda is also wanted by Everton, but Milan hope to make the most of a CSKA Moscow delay.
The Japan international is expected to leave Russia this season, as he will be out of contract in December.
The Rossoneri were in first with negotiations, but Vice-President Adriano Galliani reiterated they cannot sign anyone until the squad has been reduced.
This could let Everton in with their own swoop, but the Corriere dello Sport claims Milan can take advantage of a different delay at CSKA.
The Moscow club does not want to sell Honda until after the Russian Super Cup against Zenit on July 13.
An extra two weeks should also give Milan time to sell the likes of Robinho and Kevin-Prince Boateng.
It’s reported the Rossoneri have agreed personal terms with Honda worth €2.5m per season, but CSKA Moscow want €7m compared to the €2m proposed by the Italians.