The highly-rated teenager is not eligible to play in Italy's top flight until his 16th birthday in June, but the Rossoneri want to give him a first team chance before then.
Under current rules, no player under the age of 16 can play in Italy's top flight, but the Rossoneri are eager to add some creativity to their ranks before the end of the season.
The Italian, who is of Moroccan descent, reaches that age on June 15, 2013, but he has impressed coach Massimiliano Allegri with his exploits in Filippo Inzaghi's Primavera team.
Club CEO Adriano Galliani, with the backing of president Silvio Berlusconi, is now set to go to the authorities to ask that Mastour be allowed to represent the first team before coming of age.
Meanwhile, Milan is also weighing up a move for Javier Pastore, who has found himself on the Paris Saint-Germain bench in recent weeks, with the 2011 Serie A champions considering a swoop for him.
Another target could be Wesley Sneijder, who has been frozen out of the Inter first team squad until negotiations over his contract are concluded.
A move to either Schalke or Anzhi Makhachkala does not look likely for the former Ajax man, and Berlusconi believes that a bid of 12 million euros would convince the Nerazzurri to part with him.
Milan's 1-0 win over Juventus at San Siro on Sunday saw the club rise to ninth place in the Serie A table.