Nagelsmann, whose sacking in March 2023 led to Tuchel's arrival, was tipped to return to Bayern, but has now extended his contract with Germany until 2026
Thiem became the first Austrian since Thomas Muster in 1996 to reach the final of the claycourt tournament after subduing Murray for the first time in his career.
Just as in Friday's gruelling quarter-final with Albert Ramos-Vinolas, Murray got off to a bad start.
The Briton relied on his serve to recover the second set but could not sustain the level and bowed out.
Thiem will meet either nine-time Barcelona Open champion Rafael Nadal or Argentine Horacio Zeballos in Sunday's final.