Talks with Darmian's camp have already opened as Roma seek to bring the defender back to Italy in January.
Roma coach Eusebio di Francesco has informed Monchi they need to find a fullback signing and both have settled on Darmian as a priority, says TMW.
For his part, Darmian is keen after admitting earlier this season that returning to Serie A could be an option in 2018.
"I made a choice [to come to Manchester United] and I don't regret it," Darmian said.
"Of course it's normal that any player wants to play as much as possible. I work hard every week and I'll keep doing it.
"I don't always watch Italian football and I don't know what will happen in future, maybe there will be a chance to come back one day."