Everton manager Carlo Ancelotti has made defensive reinforcements a priority this summer, with director of football Marcel Brands tasked with signing a centre-back and right-back ahead of the new season.
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Gabriel, 22, has emerged as Everton's number one target at centre-back, with Lille ready to sell if they receive an offer in excess of £25 million.
Napoli, who are battling to hold onto Manchester City target Kalidou Koulibaly, are also interested in Gabriel, but sources have told ESPN that United's interest is the most concerning for those at Goodison.
United manager Ole Gunnar Solskjaer wants to add a centre-back to his squad this summer, but while sources have confirmed that Gabriel is a player of interest at Old Trafford, he is only one of a number of potential defensive recruits.