The Dutch midfielder was strongly linked with a switch to Old Trafford during the summer, but opted for a somewhat surprising move from Holland to Italian giants Roma.
Strootman has impressed hugely since his move to Italy, and has been an integral part of the Roma side that currently sits top of Serie A.
Manchester United are set to try and strengthen their midfield once more in January, having missed out on deals for Thiago Alcantara, Cesc Fabregas and Ander Herrera in the summer.
And Strootman’s former boss Dick Advocaat believes the Dutchman could well prove the missing link in United’s midfield.
“Strootman is a pure professional,” the Dutch coach told Algemeen Dagblad.
“It frankly surprised me that he did not get to the absolute top last summer and was on the side a little. I do not think he will stay at Roma that long. If Kevin is at this level, he will be plucked away.
“And then it will be a team of the calibre of Manchester United.”
Moyes has recently been rocked by the news he is set to be without Michael Carrick until Christmas, with the influential midfielder suffering an Achilles injury.
Marouane Fellaini has struggled since completing his £27.5million move in the summer, meaning Moyes is likely to go back into the transfer market in January.