The Bundesliga champions have made the Germany international a top transfer target this summer.
Bayern feel Sane would benefit from the regular game time he would enjoy in the Bundesliga compared to at City, where often finds himself among the substitutes.
Despite their interest a deal remains some way off with Goal revealing last month, when interest from the Allianz Arena first emerged, that the Blues remain keen on tying the Germany international to a new contract.
The cost of the transfer may also prove prohibitive with City reportedly only ready to consider a deal worth around €100 million (£88m/$112m).
If Bayern can get the deal over the line then Sule, who has played alongside Sane for the Germany national team, is confident he would be a success in Bavaria.
“Leroy is an exceptional player, Bayern Munich would do well [to sign him]. Not only because of his skills, but he is also a great guy," Sule told Sport1.de.
"I would be very happy if he came, but I do not want to get involved. But I think he knows that Bayern Munich are great.”
Sule also offered his backing to Bayern manager Niko Kovac after an up-and-down first season in charge.
Kovac led Bayern to a league and cup double but has had to deal with constant speculation about his future just a year after joining the club from Eintracht Frankfurt.
Sule, however, is convinced the Croatian is the right man for the job.
“I would not call myself a fan. He is my coach and I am professional," he added. “We had good moments and started great in the season. Then there was a dip.
“During the winter break, we all looked at each other and said: 'What are we going to do now? We have to change that!'
“We were open with him and then we came out of the difficult situation. We won the double with him despite difficult spells. That speaks for itself.
"Even in a season where there was a lot of writing about us probably not going to get a title. So it goes without saying that I give the coach my backing.”