The Mirror reports that United turned down the chance to sign Strootman for less than £10million in 2011, while the midfielder was at Utrecht.
Strootman has long been linked with a move to Old Trafford.
The 22-year-old’s agent has recently hinted that his client could leave PSV Eindhoven at the end of the season.
Strootman only signed a five-year contract when he joined PSV last year.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.