According to Germany's top-selling daily Bild and other media outlets, the 67-year-old will also quit as head of the club's supervisory board following its annual general meeting this autumn.
He is set to walk away after 40 years in charge of Bayern and reportedly has former Adidas boss Herbert Hainer, his deputy on the club's board, in mind as successor.
Hoeness joined Bayern as a player in 1970, retiring nine years later to become the club's general manager and has overseen its fortunes ever since -- apart from two years in jail for tax evasion, from June 2014 to February 2016.
The Bundesliga champions, who have just finished a tour of the USA, declined to comment when asked for confirmation by AFP subsidiary SID.
"I once said, 'It's not over yet!', but the day is not far off when I say 'That was it,'" Hoeness recently told club magazine '51'.
Bayern stars were stunned by the reports.
"First of all, I was shocked, I wasn't prepared for that," admitted left-back David Alaba following Tuesday's 1-0 win over AC Milan in Kansas City.
"I think it's unimaginable for FC Bayern to be without him.
"Regardless of whether he has a post at the club, he will always have an influence."
Defender Joshua Kimmich was equally shocked.
"I haven't heard the bomb drop yet, when is he going to quit?"
After a knee injury forced the West Germany international into retirement, Hoeness became general manager in 1979 and 30 years later was promoted to club president in 2009.
Since he first took charge in 1979, Bayern have enjoyed phenomenal success -- claiming the Bundesliga trophy 24 times, the German Cup on 14 occasions and the Champions League in 2001 and 2013.