While Favre is currently safe, doubts are emerging about the Swiss inside BVB this season.
And BILD says former Manchester United manager Mourinho has been discussed as a replacement.
Mourinho is close to BVB chief Hans-Joachim Watzke and they're in contact regularly.
This year, the Portuguese stated: "I think the Bundesliga is really interesting.
"I admire the work of BVB and its attempt to compete with a giant like Bayern."