The 23-year-old Netherlands international has been heavily linked with United, despite PSV Eindhoven's insistence that he will remain at the Eredivisie club this summer.
But Strootman himself has hinted at a move away from the Dutch giants, claiming a number of teams - including Russian sides - are keen to sign him up.
Speaking to Voetbal International, Strootman said: "There are several clubs interested but only when they reach an agreement with PSV do I come into the picture.
"This is not to say that any are in the world's top six. There is also interest from Russia, but that is not an option for me. I do not make hasty decisions about my future.
"The opinion of Holland coach Louis van Gaal is also very important with the World Cup in Brazil next year."
United are expected to strengthen in central midfield this summer, with Strootman - who impressed for the Dutch under-21s at the recent European Championships in Israel - a potential target.
United scouts reportedly monitored his progress with the national squad and PSV, and his club's failure to hang on to its best talent may see Strootman leave as well.
"It was very unfortunate that so many players left PSV," continued Strootman. "I did not expect Dries Mertens and [Erik] Pieters would leave the club."
Pieters has signed for Premier League side Stoke City, while Mertens has joined Napoli, which may led Strootman to consider his own future.