The Nerazzurri president insists he is ready to splash out on a new midfielder or striker this summer and says the Arsenal fullback's destiny is in his own hands.
Torres is widely expected to be sold by Chelsea at the end of this season and is a target for Atletico Madrid, while Dzeko has been told he can leave Manchester City in search of regular first-team football abroad. Sagna, whose current contract expries this summer, has yet to commit himself to a new deal with Arsenal.
Club director Piero Ausilio hinted earlier this month that wage demands would make any move for Torres or Dzeko difficult, but Thohir insists he is ready to splash out on a new striker.
"We'll go to great expense for a striker or a midfielder," he told Gazzetta Dello Sport. "I heard the names of Torres, [Alvaro] Morata and Dzeko. It's possible that one of them will come in.
"We like Sagna, but his future depends only on him."
When asked if Chelsea striker Samuel Eto'o could be in line for a return to the San Siro, Thohir joked: "We need a striker who is not too young nor too old."