Rossoneri chief Adriano Galliani has revealed that the club were unwilling to meet PSV's €20 million valuation and ruled out signing a striker this summer
The Dutch midfielder, 23, sealed a deal to join the Giallorossi on Wednesday on a five-year deal from PSV.
Galliani admits that Milan were pursuing Strootman but claims that his side were not willing to offer up the eight-figure sum for the 23-year-old.
"Strootman is a very strong player who we had tracked for a while, but did not have €20m for a player like him," the Rossoneri vice-president told Sky Sport.
"Roma did a great deal, though, as he is a player of the very highest level."
With the likes of Mario Balotelli, Giampaolo Pazzini, Stephan El Shaarawy and Robinho available in attack, Galliani also ruled out any summer moves for additional forwards.
“We are not looking for any strikers, because we already have players like Giampaolo Pazzini in the squad," he added.