Gattuso revealed last week that he would consider his future at the San Siro following a disappointing season that has seen the Rossoneri struggle both domestically and in Europe.
"Is it true that Gattuso wants to leave Milan? I like him," Beckenbauer told La Gazzetta dello Sport.
He added: "He would be an important figure for a successful Bayern. In fact, he would be perfect."
Beckenbauer also denied Italian media reports that in-form Bayern striker Luca Toni would return to Serie A next season.
Toni, who joined Bayern from Fiorentina last year, has been sensational in his first campaign in the Bundesliga, scoring 35 goals as Bayern clinched the domestic league and cup double and reached the semi-finals of the UEFA Cup.
The Italy international has been linked with a move to AC Milan but Beckenbauer is adamant he is going nowhere.
"We are extremely happy with Toni," said Beckenbauer.
"Toni is not for sale and, moreover, there is a clear contract.
"Toni is a goal machine. Toni will help Bayern win again as soon as possible the Champions League."