The 31-year-old right-back is out of contract at the Emirates this summer, which means Inter and any interested foreign suitor has been allowed to talk to him since January.
Thohir has now revealed that they are waiting to hear from Sagna as to whether he will be making the move to the San Siro.
Speaking to La Gazzetta dello Sport, Inter chief Thohir revealed: "I'm not used to making announcements if there is not a signed contract.
"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 is still in talks with Arsenal about a possible new deal, whilst Premier League rivals Manchester City and Chelsea have been linked with the Frenchman.
Meanwhile, Thohir spoke about other aspects of Inter's squad and revealed that they would be looking at improving their strike-force, but not with former star Samuel Eto'o, who had been linked.
However, he admitted an interest in both Fernando Torres and Edin Dzeko.
"Where we will make the most important investment? It will be made in attack or midfield. (A return of) Eto'o? In attack we have [Rodrigo] Palacio, who is over 30 and [Maruo] Icardi who is very young, so the other striker has to be in the middle age."
Asked about Dzeko, Torres and Morata he replied: "I too hear these names. Maybe one of them will really arrive. But he must respect our salary parameters."