According to the German tabloid, the Bundesliga runners-up have shown interest in bringing back the German international and the Bayern coach, Niko Kovac, is willing to accept the offer.
Hummels, 30, signed for the Bavarians in 2016 from Borussia Dortmund, who he had joined in 2008 after being at Bayern for the two previous seasons.
Last season he lost his place in the team to Niklas Sule, while next season, he will be even less low profile after the star signing of Lucas Hernandez from Atletico Madrid for 80 million euros.
Hummels, a World Cup winner with Germany in Brazil 2014, has been out of Joachim Low's Germany squad since March after having played 70 games for his country.
His contract at Bayern Munich expires in 2021 and according to the cited source, the Bavarians are willing to lower the transfer fee to 15 or 20 million euros.