A regulatory filing showed that a holding linked to Chairman Diego Della Valle had committed to buy up to 5 percent of the luxury group's shares.
The filing said one of the holdings of the Della Valle family had signed a contract with Credit Agricole Corporate and Investment bank, under which it agreed to buy up to 1.7 million Tod's shares.
Della Valle's family currently owns around 60 percent of the Italian shoes and leather goods company.
In October, Della Valle denied speculation in the Italian newspapers over a possible sale of the group, saying "if we were to do a deal, we would buy, not sell".
The shares were up 12.6 percent at 42.02 euros by 1430 GMT, outperforming a 1.5 percent rise in Milan's blue-chip index. They had dropped to 36.9 euros on Tuesday, a level last hit in June 2009.
The company, famous for its Gommino loafers, has been under pressure after it said in November that sales were still falling and a turnaround was taking longer than expected.
The company said earlier this year that a new strategy focused on more collections and classic looks would yield results from the second half of 2018.
(Reporting by Agnieszka Flak. Editing by Jane Merriman)
