Inter will think about appointing Barcelona Coach Pep Guardiola if results continue to deteriorate under Leonardo, according to La Gazzetta dello Sport.
Just three days after suffering an ignominious 3-0 defeat to Milan in the Derby della Madonnina, Inter were humiliated by Schalke.
The Champions League holders lost 5-2 at home and look distinctly unlikely to retain their crown.
Before last night's game, Inter President Massimo Moratti said: "I hope that Leo stays with us. He has a two-year contract."
However, La Gazzetta understands Leonardo's future is uncertain.
Moratti held talks with the 41-year-old until 12:40am last night to discuss the defeat.
Last week, Guardiola told Italian state broadcaster RAI that his time with Barcelona is coming to an end, alerting Inter to his availability.
Guardiola would be a dream appointment, but it's unclear whether he will continue coaching after his exit from Barcelona.
Betting on Serie A? Bet365 are offering a 100% deposit bonus, up to £200 - find out more