The France Under-21 international has been linked with a January move to the Premier League after impressing for the Ligue 1 side.
The Mail Online reports that Chelsea and United representatives were in attendance at the Coupe de la Ligue quarter-final clash on Wednesday.
Dembele scored the opening goal at the Parc Olympique Lyonnais to help his side book a place in the last four.
Chelsea are said to still be keen on the 23-year-old, despite having a bid turned down by Lyon last week.
The French giants are determined to keep hold of their star man, who has notched 10 league goals this season and 13 in all competitions.
Frank Lampard is keen to improve his forward options at Stamford Bridge now that the Blues’ transfer ban has been lifted.
And United boss Ole Gunnar Solskjaer wants to add a bigger goal threat to his side.
However, Lyon president Jean-Michel Aulas has underlined his determination to not lose the former Celtic striker.
“Moussa will not leave,” he said.
“On one hand, he wants to stay with Lyon. It's the best way for him to continue to improve his game.
“There have been offers for him and other players, but no one we want to keep will leave in January.”
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