The newspaper said it learned of Wannstedt's dismissal from defensive line coach Greg Gattuso. The assistant head coach told the newspaper the assistants were notified of Wannstedt's firing Tuesday afternoon.
School officials had not issued any comments on the report.
Wannstedt, 58, who has been at Pittsburgh since 2005, signed a two-year contract extension this year that was to keep him at the school through 2014.
The Panthers are 7-5 and are to play Kentucky in the BBVA Compass Bowl Jan. 8 in Birmingham, Ala.
Wannstedt, who also played college ball at Pittsburgh, has a 42-31 record with the Panthers. He previously coached extensively in the pros and at other colleges.