On Monday, Pearson confirmed that he was considering a move for the 33-year-old, who is now a free agent following 10 years at San Siro.
Speaking to reporters, the 50-year-old coach said that he would continue working on the deal, but admits that a number of circumstances could scupper a move for the veteran Argentine.
"I don't know about Cambiasso," he said. "I don't take too much notice of the airwaves. I've not denied our interest. It's something we will continue to work at.
"We have an interest, yes. But my view on talking on other people's players I don't. I don't have a track record of talking about speculation.
"Whether deals can or can't be done it will be based on a number of criteria. We'll work really hard to do the deals. I can't account for other circumstances intervening."
Cambiasso, who turns 34 on Monday, helped the Italian giants to five Serie A crowns, four Coppa Italia titles and a Champions League in 2010.
The Foxes are preparing for their first Premier League game for more than a decade after Pearson guided them to promotion via winning the Championship last season.