The Dutchman has just over 12 months remaining on his Inter deal, and he could be sold for a knockdown fee this summer.
Chelsea were linked with his services earlier this summer, and Corriere della Serra cites that United are also keen on landing him.
The Red Devils are eyeing a young central defender to add to their ranks, but are yet to make any progress in the transfer market.
They have been linked with Jurrien Timber and Lisandro Martinez from Ajax, but both will cost at least €60 million to purchase.
With the huge outlay required, they may be tempted to pursue a short-term signing. De Vrij could be an ideal candidate for that role.
He has vast experience at the highest level. He is strong in the air and has impressed with his tackling and ability to clear his lines.
He could be purchased for around €15m this summer.