Umtiti is believed to be a top target for Jose Mourinho and United as the 24-year-old France international reportedly pushes for a new contract at Barca.
Asked about links to United, Umtiti – who revealed discussions over a new Barca deal have not started – told Canal+: "There is interest from several clubs but, I said it again, I have so many objectives to reach with Barcelona that for the moment the question does not arise.
"In this world, it goes very fast. But what I can say is that I am very happy."
"My future is a subject that I don't want to talk about too much," he added. "I haven't started anything yet. Maybe there is an interest from Barca [for an extension], but nothing has started."
Umtiti's buyout clause is set at €60 million, making him an appealing target for clubs throughout Europe.
"A payout clause does not mean much, everyone is aware of it," Umtiti said.
"It concerns me, but it does not interest me. I am interested by [what I do on] the pitch and have fun."