The Rossoneri have been following the highly rated midfielder for quite a while and are now ready to step up their interest.
Milan sporting director Ariedo Braida watched the player in the Europa League clash between PSV and Napoli, with Strootman impressing alongside former Milan midfielder Mark van Bommel in midfield.
The Italian giants are hoping Mark van Bommel can help them persuade the player that his future lies at San Siro.
Strootman, who has just been named Netherlands captain by coach Louis van Gaal, is also followed by Barcelona, Real Madrid, Inter and Manchester United.
The 22-year-old is widely regarded as one of the most talented midfielders in world football and he is already considered a key player for both club and country.
In total, Strootman has made 38 Eredivisie appearances for PSV since arriving from Utrecht, and scored 3 goals.