The 21-year-old Frenchman is one of the most highly rated defenders in Europe and has courted interest from the likes of Arsenal, Manchester City and Paris Saint Germain.
Upamecano’s current deal at the Red Bull Arena expires in the summer of 2021 and it is believed he has a release clause of €60m which will expire later this month.
Upamecano will be able to walk away for free next summer if he does not sign a new deal but Leipzig sporting director Oliver Mintzlaff is not prepared to see that happen.
“Upa is an extremely important player for us and one of the most sought-after talents in his position,” Mintzlaff told Bild.
“One thing we can assure you of is that we have a very clear understanding with him and his agent that he will not be allowed to leave for free.
"We can’t afford that as a club.
“There are two options for him – he will either sign a contract extension or leave.
"I’m sure that we will know relatively quickly in which direction it goes.”
Upamecano has made 25 Bundesliga appearances this season, with Leipzig currently occupying third position on the league table.
Leipzig have also secured a place in the quarterfinals of the UEFA Champions League after overcoming the challenge of Tottenham Hotspur in the round of 16.