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.
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.
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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