The Italian giants have made nine first-team signings this summer, but they continue with their pursuit of a high-profile forward before they attempt to mount a challenge for the Serie A title.
Fassone told Sky Sport Italia: "We continue talking about a striker, but must use our time wisely. We're working on it, there mustn't be any sense of haste, as we don't want to make a mistake.
"So far I haven't said no to any of the names that have been mentioned, and I won't say no to Falcao either, but among the six or seven names that have been suggested we've been closer to some than others."
Last season, the Colombian international netted 30 goals from 43 appearances in all competitions.