The Mirror says United will be kicking themselves for turning down the chance to sign midfielder Strootman for less than £10m in 2011, when he was at Utrecht.
Strootman has been on United's radar for over a year and is understood to be keen on the prospect of a move to Old Trafford.
The 22-year-old's agent has hinted a transfer could happen at the end of the season. But United face a big battle over the fee, particularly if they try to force a January deal.
Strootman only signed a five-year contract to join PSV last year.
It is understood United are hoping to sign him for around £15m.