The 31-year-old is out of contract at the Emirates Stadium at the end of the season.
The Gunners are said to be in talks with the France international over a new deal, but Thohir has revealed that he is waiting to hear from Sagna as to whether he will make the move to Serie A.
"I'm not used to making announcements if there is not a signed contract," he told La Gazzetta dello Sport.
"I can only say that we like Sagna and that at this point it all depends on him. If he does not arrive, we will take a younger right-back."
Sagna joined Arsenal from Auxerre back in July 2007.