Tuttosport claims Marco Giampaolo has until the next national break to convince Torino, lining up Davide Nicola and Roberto Donadoni as possible alternatives.
Torino sit bottom of Serie A after three games and three defeats, conceding eight goals in the process.
Marco Giampaolo was brought in during the summer to replace Moreno Longo at the helm, but the Turin-based newspaper claims the next five games could prove decisive for the new tactician.
The Granata travel to Sassuolo tomorrow night, facing a high-flying Neroverdi, still unbeaten and second in Serie A after four games.
Then, a Coppa Italia appointment with Lecce follows, before League games against Lazio, Genoa and Crotone ahead of the next international break in November.
The newspaper reports the club has not considered parting ways with Giampaolo, who lost his job at Milan after seven games last term.
But the report claims Donadoni and Nicola are alternatives for Davide Vagnati and Urbano Cairo, and a return for Longo has not been ruled out.