The French striker, who is being followed by several Premier League clubs, has enjoyed a productive first season with the Ligue 1 side, scoring 23 goals in all competitions since his move from Celtic.
That has prompted United to make an initial offer worth around €40m as Ole Gunnar Solskjaer looks to improve his attack following a disappointing 2018-19 campaign.
Goal understands that the Red Devils have been following Dembele since his youth days at Paris Saint-Germain, with club ambassador Eric Cantona having endorsed the move for his fellow Frenchman.
Dembele is contracted to Lyon until 2021 meaning the Ligue 1 side, who secured Champions League football for next season with their 4-0 win over Caen last time out, are in a strong position in negotiations.
It remains to be seen how attracted the 22-year-old is to a move to Old Trafford, however, with Solskjaer’s side having to settle for a place in the Europa League after finishing sixth in the Premier League table.
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