United and Italian giants Inter Milan have both been linked to the midfielder, 29, this summer.
According to The Athletic journalist David Ornstein, United are among the clubs that would snap up Kante.
Should he leave Chelsea, the midfielder would stay in the Premier League.
Club owner Roman Abramovich reportedly "loves" Kante.
Ornstein added: "And when he loves a player, he does not want to let them go."
Reports had claimed Chelsea would entertain offers around £55million for Kante.