The defender has entered the final year of his contract at the German giants and his situation has seen him attract interest from elsewhere.
Premier League side Newcastle, financially rejuvenated with the arrival of new owners, have been linked with the Germany international ahead of the January transfer window.
However, Bayern Munich are keen on keeping the centre-back and have offered him a new contract which is tipped to be worth €10m a year, more than the €8m he is currently earning.
And according to German daily Bild, the Bavarians are optimistic there is a good chance Sule will put pen-to-paper on improved terms.
With Sule yet to commit to a new deal at the Allianz Arena, his entourage are claimed to have offered him to other clubs while the Magpies are floated as a potential destination.
New Newcastle boss Eddie Howe has been evaluating his squad and has had discussions with the club’s hierarchy where they need to bring in fresh faces.
It remains to be seen whether Sule will extend his stint at Bayern Munich or opt for another challenge, which Newcastle could present him with.