The 23-year-old has made a flying start to his Serie A career as Rudi Garcia's men have emerged as surprise challengers to Juventus' league title defense.
United, meanwhile, has labored this season with obvious weaknesses in the center of the pitch, despite the 27.5 million pound signing of Marouane Fellaini from Everton in the summer.
But Strootman's agent Chiel Dekker insists his client has no desire to leave the Italian capital anytime soon.
"Kevin is very happy in Rome and his intention is to stay here for a long time," Dekker told Sky Sports. "They have started a project and a new team and he has adapted well to his new club."
Strootman has managed three goals and five assists in 14 Serie A appearances for Roma this season, with the Giallorossi yet to lose a game in the Italian top flight.