The 43-time Netherlands international joined the Ligue 1 outfit last summer for £23 million after five seasons with Roma.
Sky Sports report that l'OM have offered the 29-year-old to the three Premier League clubs after he was previously linked with a move to Old Trafford during the reigns of David Moyes and Louis van Gaal.
Strootman has featured regularly this season, making 27 league appearances, but it was announced this week that manager Rudi Garcia will leave at the end of the season after failing to secure European qualification.
Marseille are in sixth place with one round of fixtures remaining and are looking to trim their wage bill over the summer.
Big changes are expected at United this summer after a disappointing campaign, and the report says that the club has already agreed personal terms to sign 20-year-old Swansea winger Daniel James as they focus on youth.
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