Manchester United are racing to get a number of deals done before Thursday’s 5pm deadline.
And shock reports from France suggest the Red Devils have made an offer for Lyon striker Dembele.
It is unclear how much the Ligue 1 side would demand for the 23-year-old, who has hit 20 goals in 26 starts.
Yahoo Sports’ France reporter Manu Lonjon confirmed on Twitter that United have made a bid for Dembele.
He wrote: “English offer for M Dembele (OL)! It would be Manu Utd!”
It is well known Ole Gunnar Solskjaer is keen to add attacking reinforcements.
Romelu Lukaku has returned to his native Belgium to train with Anderlecht as he attempts to force a move away from Old Trafford.
Juventus and Inter Milan are keen on signing the powerhouse but are reluctant to meet his £75million price tag.
United were in talks to sign Paulo Dybala and Mario Mandzukic from Juventus.
But after several days of negotiating in London the Red Devils pulled the plug on a deal for the Argentine.
There is still plenty of business to be done in the north west as Solskjaer faces a fight to keep hold of Paul Pogba.
Real Madrid are keen on taking the France international to the Bernabeu but are also put off by his price tag.
Meanwhile, United see either Tottenham’s Christian Eriksen or Sporting Lisbon’s Bruno Fernandes as ideal replacements.
But moves for the midfield duo would rely on those clubs first finding a replacement.
And with English clubs now into the final 48 hours of the transfer window, pressure is increasing on senior club executives.