With Chelsea manager Jose Mourinho reportedly keen on bringing Atletico Madrid striker Diego Costa to Stamford Bridge next season, Torres is widely expected to leave the London-based Premier League club.
The 30-year-old Spaniard has never fully settled at Chelsea since joining from Liverpool for a reported fee of £50 million and Inter could be set to offer Torres a chance at proving his critics wrong in Serie A.
"He is one of the names that interest us," Fassone told Radio Deejay.
"Our President Erick Thohir admitted as much in recent days.
"You will discover in due course who the player is that we will focus on."
Inter have already captured the signature of Manchester United defender Nemanja Vidic for next season, as they look to build a squad that can challenge for their first Serie A title since 2010/11.
The Milan-based club sit fifth in Italy's top tier with five games remaining, which would be enough to qualify for next season's UEFA Europa League, which Fassone rates as a top priority after Inter did not compete at a continental level this campaign.
"Our goal at the moment is to get into the Europa League. It would be a problem if a club like Inter did not play in Europe for two successive seasons," Fassone said.
Inter have also been linked with Manchester City striker Edin Dzeko and young Real Madrid forward Alvaro Morata.
Arsenal are also rumoured to be interested in Morata with the Spanish striker's agent Juanma Lopez confirming on Monday that Real Madrid have not offered the 21-year-old a new contract, with his current deal expiring in June 2015.
"Could Inter step up their interest in him? I won't rule it out, it is a possibility," Lopez told calciomercato.com.
"Will he play for Inter next season? It could be, anything could happen. There's no news on a Real Madrid contract renewal."
Morata has played 28 matches in all competitions for Real this season, scoring seven goals.
