Ronaldo has told Manchester United he wishes to leave amid concerns he will be unable to compete for the biggest trophies at Old Trafford.
Although the Red Devils insist he is not for the sale, the 37-year-old has asked them to accept any suitable offer that comes in.
"Ronaldo to Bayern would be sexy!" Matthaus told Sky Deutschland. "At least you should think through the options and play through them once.
"If Bayern are of the opinion that Cristiano Ronaldo is still physically able to really help for a year or two and that they can invest the transfer fee generated for Robert Lewandowski more or less like-for-like in the Portuguese megastar, I would think about it."
While Matthaus would have some concerns over Bayern buying the United star, he believes they are outweighed by the impact he would have on and off the pitch.
"Of course, that would not be a transfer with a view to the future," he said. "He's 37 and would always make headlines.
"I'm also not sure if he fits into Bayern Munich's system. But he's still an outstanding goalscorer. He's one of the best strikers of all time and would certainly score around 30 goals. Refinancing through jersey sales and the like would be guaranteed."