Reports in Italy claim Juventus' inability to beat Catania on Saturday spells the end for Gigi Del Neri.
Juventus led 2-0 in Turin but lost their heads in the last 10 minutes and conceded twice to draw 2-2.
Although unbeaten in five matches, Juventus lie seventh in Serie A and risk missing out on Europe.
La Repubblica understands Juventus President Andrea Agnelli has told the club's general manager Beppe Marotta to start looking for a new Coach before next season.
Del Neri has apparently disappointed them for failing to get the best out of a squad that they consider to be rather good from a technical point of view.
Luciano Spalletti, Walter Mazzarri and Roberto Mancini are the favourites for the job in Turin.
However, all three remain under contract and would prove difficult to appoint.