The 27-year-old has made just 15 appearances for United this season having fallen behind Ashley Young and Luke Shaw in the Old Trafford pecking order.
Blind’s contract at United has been extended until 2019 but Jose Mourinho could still allow the player to leave.
Roma are looking to replace Emerson Palmieri, who joined Chelsea in a £17.6m on Monday.
Zlatan Ibrahimovic continues to be linked with a move to LA Galaxy, though a move is far more likely to go through at a later date.
Ibrahimovic will still be able to leave Old Trafford after Wednesday’s deadline as the Major League Soccer transfer window only opens on 7 February.
Galaxy head coach Sigi Schmid has insisted that talk of the 36-year-old moving Stateside remains speculation, though he admitted to interest on Galaxy’s side.
“There’s been a lot of talk about it in the past and it’s something that maybe gets opened up again,” Schmid said.
“I don’t know what’s there. If there was something there, I’m sure we’d all know. Right now, it’s all rumours.”
United are otherwise expected to be quiet on transfer deadline day, with Mourinho claiming after the signing of Alexis Sanchez that little more business would be done.
“Nobody is leaving, nobody is coming,” the United manager said a week ago. “Our transfer market in the summer will be short.”
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