Manchester United are reported to have sent a scout to watch striker Dembele in Tuesday's Coupe de la Ligue semi-final clash with Lille, the 23-year-old scoring a first-half penalty and then converting his spot-kick in a shoot-out as Lyon edged through.
Dembele, who has also been linked with Chelsea and Tottenham, joined Lyon in 2018 and is in no rush to leave.
He told reporters after the game: "I am a Lyon player and I will remain so until the end of the season.
"I do not think that there will be a departure this winter. Lots of things are being said but it's up to me to ignore that and remain concentrated on the pitch."
The news will come as a blow to United in particular with Ole Gunnar Solskjaer thought to be keen to bolster his attacking options.
Marcus Rashford is out for at least two months with a double stress fracture in his back while the club have yet to replace Romelu Lukaku and Alexis Sanchez, both of whom joined Inter over the close season, the latter on loan.
Dembele's stance will also please Lyon president Jean-Michel Aulas, who, speaking earlier this month, was adamant the former Celtic man would not be leaving the Groupama Stadium.
He said: "Moussa Dembele will not leave because he wants to stay and win something with OL.
"There have been offers for him and for other players, but none of those whom we want to keep will leave in January."