Torres continues to be linked with a summer move away from Chelsea despite Jose Mourinho recently declaring that he has a future at Stamford Bridge.
The Spanish striker has also made it clear that he remains committed to seeing out the final two years of his contract, even though he has struggled to hold down a regular starting spot this season due to inconsistent form.
Inter president Erick Thohir has previously admitted that Torres would be a good signing for the Italian club, and Fassone says he is still very much on their radar.
However, Fassone has insisted that Inter are currently mulling over a lot of options and have yet to decide who they will make their top target.
Inter's current focus is on making sure they qualify for the Europa League, having finished a disappointing ninth in Serie A last season.
Speaking about Torres, Fassone told Radio Deejay: "He is one of the names that interest us, as admitted by our president Erick Thohir in recent days.
"Then you will discover in due time who will be the player we will focus on.
"Now our goal is to get a place in the Europa League.
"It would be a problem not to play in Europe for two consecutive seasons."
Inter are currently fifth in Serie A and, with a UEFA Champions League spot out of reach, must ensure they hold on to a place in the top six to qualify for the Europa League.