Both Ole Gunnar Solkskjaer and Pep Guardiola are keen to bring in a world class defender this summer, although the latter is apparently prioritising Kalidou Koulibaly of Napoli.
The Manchester sides had identified Upamecano as an option after watching him closely over the past year, with the Frenchman's stellar performances in the Champions League only adding to his reputation.
However, it looks like their pursuit will be fruitless, with the central defender set to stay in Leipzig.
"He [Upamecano] will be here for the season. I'm sure about that," Nagelsmann told ESPN.
The RB Leipzig boss did concede that he expects Upamecano to leave eventually due to his talent.
"As for the future, I'm not sure as he is very talented. Lots of club will want to buy -- perhaps next season it could be real that he leaves the club. But this season he will stay."
Leipzig's star player over the past few years, Timo Werner, has already left the club this summer to join Chelsea in a big money deal.
Nagelsmann has faith that players of that calibre can be replaced, though.
"It is normal when you work with young guys that clubs will try and find young talented guys in the transfer market," the 33-year-old added.
"It is normal that bigger clubs will try and buy these players.
"You have to deal with that, you've got to be one step forward when you buy new players or find new players. Our scouting should be good and we have made a lot of good decisions in the transfer market."
Leipzig made it to the Champions League semi-final for the first time in their history in 2019/20, but were eliminated by Paris Saint-Germain.