The striker is reported to have recently gone on strike in an attempt to force a move to West Ham United, who have also been linked with the player.
Ba had a phenomenal season with Hoffenheim following their promotion to the Bundesliga, scoring 14 goals including a hat-trick against Stuttgart.
The former Watford trainee joined the German outfit forom Belgian club, Mouscron. He helped Hoffe reach promotion in 2008 and been an integral part of their first team since.
Stoke appear to be in the market for a striker to support Kenwyne Jones and Ricardo Fuller with rumours coming out of the Britannia Stadium that Turkish forward Tuncay may be set to leave The Potters.
Hoffenheim may be forced to sell if Ba refuses to play for the German outfit, but they have promised to punish the striker should he continue to act out and expect Ba to honour his current contract which expires in 2013.