Barcelona appear favourites to snap up the 29-year-old Germany international on a free tranafer but Matthaus has urged Bayern to move quickly so the player can remain in the Bundesliga.
Matthaus said: "Bayern made a mistake last summer by not signing Tah. But maybe this time he'll decide to play in Munich. There's a lot of uncertainty in defense and Tah would be a big help.
"Bayern isn't happy with Kim, although I rate him as a centre-back. But maybe he needs a leader next to him. Tah would be one of those.
"If I had to advise FC Bayern, I'd say they need the best — and Tah is one of the best. I'd definitely negotiate for Tah."
Tah's departure marks the end of an era for Leverkusen, where he rose through the youth ranks to make over 300 appearances since his debut in 2015.
He said: "I've been completely transparent with the club. There's no set timeline, but they've known my intentions from the start.
"I decided not to renew my contract or stay here, and that hasn't changed."
Fiorentina have reportedly intensified their pursuit of Bayern Munich icon Thomas Muller, while Bayern are actively looking to part ways with defender Sacha Boey, with Galatasaray circling for a potential return.
Bayer Leverkusen's stalwart defender Jonathan Tah has confirmed he will leave the club when his contract expires at the end of the 2024-25 Bundesliga season.
Vincent Kompany praised his Bayern Munich side for putting in a "complete" performance after beating Heidenheim 4-0 to go eight points clear at the top of the Bundesliga standings.
Harry Kane was on the scoresheet yet again as Bayern Munich made short work of Heidenheim on their seemingly unstoppable march to the Bundesliga title.
