Citing reports from Italian newspaper La Gazzetta dello Sport, the article claims Roma rejected United's opening offer for the talented central midfielder last month. They want at least €40m for the player they signed last summer from PSV Eindhoven.
United's offer was reportedly worth €25m plus bonuses depending on performance, but the Italian giants are desperate to keep Strootman in Rome.
United boss David Moyes has been heavily linked with a number of central midfielders, but his only purchase in the Janaury window was the £37m acquisition of playmaker Juan Mata.
Strootman was mentioned as a United target last summer before he moved to Roma. The defending Premier League champions either missed out or dropped out of the race.
They seemed to have realised their mistake now though, with the report claiming a bid had been made by United, although it was swiftly rebuffed.
Roma trail league leaders Juventus by nine points in Serie A, but they have a game in hand on the Turin side.
Strootman has been one of the club's most impressive performers - according to whoscored.com he's been their second best player this season providing five goals and six assists.