Watford have announced the signing of Italy international Marco Motta, subject to international clearance.
Mark Noble has signed a new deal with West Ham which will keep him at the club until the summer of 2020.
Muller and Kurz, along with his assistant Gunther Gorenzel, were relieved of their duties, with Markus Gisdol taking charge of first-team affairs with immediate effect.
Kurz has been in charge for just three months after succeeding Markus Babbel in January but failed to improve the team's fortunes.
Hoffenheim are second from bottom in the Bundesliga having won just two of Kurz's matches in charge.
The Baden-Wurttemberg club are four points from a relegation play-off spot and nine adrift of safety.
Kurz's final game in charge was a 3-0 defeat at Schalke on Saturday.
Gisdol, who will be presented this afternoon, will be on the bench for Friday's home game with Fortuna Dusseldorf.