The 20-year-old made a name for himself by helping the French club to a surprise second-place finish in Ligue 1 last season.
And he is now at the centre of a transfer battle between Premier League giants United and Spurs, the Sun reports.
Both clubs are in talks for the youngster about a January move, but he has peaked the interest of teams across Europe.
"It is true that there is a lot of interest from Spain, from Italy,” said Lille president Gerard Lopez.
"The interest of Jose Mourinho? I know he likes him very much, yes.
"There are five or six clubs that are interested in him so we will see."
Mourinho’s connections could give him a boost in his pursuit of Soumare, as his assistant Joao Sacramento was at Lille until joining the Portuguese’s staff in north London last month.
Napoli, Real Madrid and Valencia are among the other clubs believed to be interested.
But the France Under-21 international won’t come cheap, as he is valued at £40-50 million and has a contract until 2022.
Soumare has made 22 appearances in all competitions for Lille this season, including six Champions League outings.
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