Traore previously played under Jose Mourinho at Chelsea, making his debut in English football under the Portuguese manager in September 2015.
However, the Burkina Faso international failed to nail down a regular starting role at Stamford Bridge, being sent out on loan to Vitesse and Ajax before joining Lyon for £6m on a permanent basis during the summer.
Traore has since scored six goals in 16 appearances across all competitions this season, and a number of Europe's top clubs are understood to be monitoring the winger.
French football magazine Onze Mundial claims that Mourinho's United are amongst those keeping tabs on the 22-year-old ahead of a possible January swoop.
Mourinho is understood to be keen to add more attacking width to his squad, although reports have suggested that he will need to sell players in order to raise funds for any new signings he identifies.