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Alaba’s departure is not yet arranged but it appears Bayern will move quickly to bring in a top-level replacement, with Upamecano one of the world’s most highly-rated young defenders.
The 22-year-old is nearing 100 Bundesliga appearances for Leipzig since his move from Red Bull Salzburg in 2017, and he made his senior international debut for France last year.
Speaking on Bild Live, Rummenigge said Upamecano would remain at Leipzig at least until the end of the season, so it was too early to say he would definitely be joining Bayern.
“We will of course deal with it, not only with this player, but in principle,” Rummenigge said, “on the positions where we want to do and have to do something.”
The Bayern chief also noted it was common knowledge that Upamecano has a release clause in his Leipzig contract. He signed a new deal to 2023 last year, with the clause reportedly worth around €45 million (£40m/$55m).
"In the time of Corona, the money situation is also an important factor,” Rummenigge added.
Bayern are four points clear of second-placed Leipzig at the top of the table after both sides recorded narrow victories on Wednesday.
Defender Jerome Boateng has earned praise for his performances this season and there have been rumours that the 32-year-old could be set for a new contract.
However, Rummenigge refused to be drawn on such speculation.
“Jerome is playing an important role again. The coach is happy with him,” he said. “Accordingly, you will have to ask him this question yourself if you speak to him.”
Rummenigge was also keen to quash rumours suggesting Bayern could be considering selling Leroy Sane, who has four goals and five assists from 15 Bundesliga appearances so far this season.