The Tottenham midfielder is in the final year of his contract in north London and has been linked with a move to Bavaria.
Eriksen, who has also attracted the interest of Real Madrid, will be free to arrange pre-contract terms to join a new club on a free transfer in January.
Sport1 reports that the Dane would be open to a move to Munich and that Bayern have retained their interest in the playmaker after making enquiries in recent months.
But Matthaus, who won seven Bundesliga titles with the club as a player, believes that his former employers would be better off making a move for Bayer Leverkusen youngster Kai Havertz.
“I’ve been following the player for a long time and so far in 2019 he has disappointed me,” Matthaus said.
“A transfer to FC Bayern wouldn’t make sense in my view, and would be very surprising.
“If he’s not enough for Tottenham, he’s not good enough for Bayern. Uli Hoeness has also said before that Bayern doesn’t need any substitutes.
“Eriksen is a fine technician, a typical No.10, but he’s too slow and Niko Kovac likes fast players.
“In my view, Eriksen isn’t a player who can make the difference at the highest level. This coming summer, they should instead concentrate completely on the transfer of Kai Havertz.
“They also still have Philippe Coutinho, too, who plays outstandingly as a 10.
“You also can’t forget Thomas Müller, who can play every offensive position and shouldn't be let go. I stand by my opinion: Eriksen makes no sense to me.”
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