Speaking on Sky 90, Matthaus advised against the move for the young Bayer Leverkusen star, suggesting he should remain under the tutelage of Xabi Alonso.
"I would not go to Real Madrid," Matthaus said. "He's still young and can learn a lot with Xabi Alonso if he stays in Leverkusen."
However, he was less certain about Wirtz joining Bayern Munich next season, adding, "I think it's possible financially, but does he want to go to Bayern?"
The 21-year-old Wirtz is contracted to Leverkusen until 2027. Matthaus believes Wirtz might stay with the club at least until the 2026 World Cup, which will be held in Canada, the United States, and Mexico.
"I have the feeling that Wirtz will remain in Leverkusen until the 2026 World Cup," he added.
Discussing potential fit at Bayern, Matthaus raised concerns about how Wirtz would complement Jamal Musiala, given their similar playing styles. "They are similar players. Bayern Munich has a system with two wingers and a number ten.
"Wirtz would have to play more centrally, which is where Musiala operates," he explained.
Uli Hoeness, former Bayern Munich president, also commented on Wirtz's future, noting the interest from multiple clubs. "If Wirtz is looking for a new challenge, he can choose a club. Besides Bayern, Real Madrid and Manchester City are interested in signing him," Hoeness said.
He did not rule out Wirtz staying with Leverkusen, stating, "Will he stay at Leverkusen? That's not ruled out; his contract runs until 2027."
Bayern Munich have made a blistering start to the 2025/2026 season under head coach Vincent Kompany, whose side have rewritten European football history with a remarkable 16-game winning streak.
Real Madrid's hierarchy are growing uneasy over the team's sudden dip in form but remain confident that head coach Xabi Alonso can restore balance after a turbulent fortnight.
Germany coach Julian Nagelsmann has urged Bayern Munich's 17-year-old talent Lennart Karl to focus on development with the under-21 side before thinking about a senior national team call-up.
Bayern Munich's teenage winger Wisdom Mike has played down the growing media attention surrounding his rapid rise, insisting he is focused purely on improving his game and earning his place at the club.
