The Bavarians are reportedly set to lose the services of David Alaba to Real Madrid at the end of the season on a free transfer.
With the club not looking to bolster their squad in the January transfer, Rummenigge has confirmed they will look at Upamecano and other options for next season.
"We will, of course, deal with it, not only with this player, but in principle with all the positions where we want and need to do something," he told Bild.
Asked about securing an early agreement for the defender, the Bayern CEO added, "It's too early for something like that, he's still a Leipzig player at least until the end of the season.
"But it's common knowledge that he has a clause in his contract."
The France international has also been linked with Premier League duo Manchester United and Liverpool as well LaLiga champions Real Madrid.
