United is reportedly eyeing a move for Leipzig defender Upamecano, who has also been linked with the likes of Real Madrid, Bayern Munich and Arsenal.
The 21-year-old centre-back extended his Leipzig contract at the end of July, tying him to the Bundesliga outfit until 2023.
Set to earn his first France cap as the world champions prepare to face Sweden in Saturday's Nations League fixture, Upamecano addressed the speculation.
"I extended my contract with Leipzig because I feel good with my team-mates," Upamecano said.
"My coach is giving me confidence. He's learning as well, but he gives me confidence and it improves my level.
"I've been in Leipzig for more than three years, I feel good. I've been in demand, I talked to some clubs, it's true, but I'm not in a hurry.
"We'll see what happens in the future."
Upamecano earned plenty of admirers following his exploits for Leipzig during their memorable run to the Champions League semi-finals.
The Frenchman was particularly impressive against Atletico Madrid in the quarter-finals, nullifying Diego Costa and Alvaro Morata.
"Obviously when you play a Champions League semi-final, your status changes, especially because it was the first semis for Leipzig. We wrote history," he added.
"When I was in Portugal, I wasn't paying attention to what happened outside of it until the end. Because I didn't play in Ligue 1, I was just in academies in France, I became known in Germany."