Now inside the final 18 months of his Bayern contract, his personal demands are proving too rich for the board.
With doubts over his injury record and weight issues, Bayern are prepared to sell the Germany international this summer.
Blues boss Thomas Tuchel is a big fan of Sule and is keen to bring him to London.
Sule, standing at 6ft 4in, is astonishingly quick for his size - behind only Canadian speedster Alphonso Davies as the fastest player at the club.
- updated April 20