Sane has proven his worth at Manchester City, having helped Pep Guardiola's side to two Premier League titles in the last three seasons.
But the 23-year-old fell out of favour with City in the back half of last season, starting just five matches in the league after January.
Bayern Munich have been tipped as a potential destination for Sane, with the club's chairman Karl-Heinz Rummenigge admitting that his side are looking to find an agreement for the Germany international.
Matthaus, who starred for Bayern and Germany during his playing career, believes the conditions are there for a transfer to happen.
"I really think Bayern Munich [would] like to spend a lot of money, more than €80 million (£72m/$90m)," Matthaus told ESPN. "In City he's not happy in one way, and City is ready to give him up. But the main answer has to be from Leroy Sane. Does he like to come to Bayern Munich, yes or no?"
Should Sane decide he wants to join Bayern, Matthaus believes that the club's good relationship with its former manager will help make the transfer a reality.
"When he says yes, Bayern will contact Manchester City," Matthaus said. "There's a good relationship between Bayern Munich's board and Pep Guardiola and I think they will find a way."
If Sane does move to the Bundesliga champions, Matthaus believes that the sky is the limit for the winger back in his native country.
"The important thing is Leroy Sane has to say 100 percent yes to Bayern Munich," Matthaus said.
"And then he will be a big star in Germany, maybe the biggest face of German football in the last years because for the money that Bayern would like to spend on him, he can be the new face of Bayern Munich."
However, Guardiola doesn't appear willing to let Sane leave without a fight, saying on Wednesday that he wants to help the winger reach his potential at City.