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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.