Diaz signed for Bayern on Wednesday in a €75m move.
However, Matthaus wrote for Sky Deutschland: "Luis Díaz has shown his quality in the Premier League. He's quick and powerful in duels. With him, Bayern have more options in attack. He played as a left winger, central midfielder, and second striker at Liverpool. He could play behind Kane at Bayern, like Gnabry or Olise.
"Bayern Munich has to give their all every now and then. If you want to compete at the highest level, you have to pay high salaries.
"In Munich, he will earn much more."
But the former German midfielder, now a TV commentator, then compared the 28-year-old Colombian to the case of Nick Woltemade, the young Stuttgart striker.
He also wrote: "Diaz is already 28, while Nick Woltemade is only 23. If you pay €75 million for a player five years older, you have to have a lot of faith in Diaz. If someone were critical, they might ask: why don't Bayern have the same faith in Woltemade? Stuttgart would probably have been satisfied with the amount they paid for Diaz."