Upamecano, 26, will be out of contract at Bayern at the end of the season, with talks over a new deal stalling due to his wage demands.
It’s understood that the centre-back is pushing for a package worth around €15 million per year along with a hefty signing bonus, which Bayern are reluctant to agree.
Bayern are not said to be preparing for life without the Frenchman and have identified Borussia Dortmund star Nico Schlotterbeck as the ideal replacement.
Former Bayern and Germany midfielder Matthaus has made his stance on a potential clear, the Bavarians need to act quickly.
"If things don't work out with Upamecano, then Schlotterbeck would definitely be more than an alternative. Then bringing him to Munich would almost be a must," Matthaus said.
"Because he's familiar with the Bundesliga, because he plays alongside Tah on the national team."
He added: "That would make sense to me, because his contract wouldn't run as long. But it might be a bit cheaper than with (Nick) Woltemade... Price tag, price tag, yes, thin ice.
“But that's the contract term, you have to take that into account. That's why I say: Yes, Schlotterbeck would be cheaper than Woltemade!"