The Argentine was the victim of a rash tackle in the Turin derby on Sunday and is unlikely to feature in the Bianconeri's latest European encounter
The striker was caught by a poor tackle from Torino forward Ciro Immobile on Sunday, leaving the 29-year-old with a badly cut ankle and his coach with a selection dilemma.
Conte told reporters: "Tevez did not train today. We won't take a risk with a player who cannot train. We will see how he is tomorrow."
The Bianconeri chief must also choose between Paul Pogba and the fit again Claudio Marchisio to play alongside Arturo Vidal and Andrea Pirlo in midfield.
"I will make other decisions based on training tomorrow," Conte continued.
"I also have some doubt in midfield and maybe one of those players needs a rest. Both Pogba and Marchisio have played a lot and we'll see who we rest."
Galatasaray named former Manchester City and Inter boss Roberto Mancini as Fatih Terim's successor on Monday and Conte admits he will be glad to be reacquainted with his compatriot on Tuesday.
"I am very pleased to find in Roberto back in the dug-out, we speak of an Italian technician that is good for our football and who has won everywhere he has been," said the 44-year-old.
"I would have preferred not to meet tomorrow, however, because he will create problems for us."