Matteo Darmian has suitors in Italy but Manchester United want to keep the defender beyond January, according to his agent, Tullio Tinti.
The full-back has started just one of United's last 12 games and has only started two Premier League games all season.
His agent has said there is interest from Serie A, but insists United do not want to sell the defender they signed from Torino for £12.7 million in 2015.
Tinti told Rete Sport: "I've never received any calls from Roma [for Darmian].
"There's contact with other Serie A sides, but not with the Giallorossi. At the moment, the lad's not for sale."
Darmian, 28, has slipped down the pecking order under Jose Mourinho with Antonio Valencia established at right-back and Ashley Young preferred at left-back.
Sources have told ESPN FC that Mourinho does not feel his squad is big enough to cope with any departures in January.
However, if a player makes it clear they want to leave Old Trafford then any suitable offers will be considered.
Mourinho is already having to deal with a number of injuries and suspensions at the back.
Valencia and Eric Bailly are currently sidelined while Chris Smalling is not fully fit after suffering a groin injury before Christmas.
Young will also miss the next two games against Derby and Stoke while he serves an FA ban for an elbow on Dusan Tadic during the 0-0 draw with Southampton on Saturday.