Current United shot-stopper Andre Onana is under immense scrutiny thanks to a slew of high-profile errors since joining.
Ruben Amorim is understood to be losing patience with the Cameroon international and is urging the club to sign a new ‘keeper in the upcoming transfer window.
Chevalier, 23, has impressed with Lille this season, establishing himself as one of Europe’s best young goalkeeping talents.
He has since opened the door to a move to the Premier League admitting he ‘dreams’ of playing in the English top flight.
He said, via Sport Witness: "The Premier League? It’s a league that makes you dream, the most attractive. When you see Tottenham, Manchester United struggling with crazy players, you can see the level a bit.
“I have a two-year contract, and you know the president (Oliver Letang). I haven’t had any specific offers from this country, but it makes you think."