Three years ago, the former AC Milan midfielder was the subject of negotiations between the two clubs, and the Italian international looked set follow his old manager Carlo Ancelotti to the Premier League.
Not only were the two clubs in talks, Pirlo himself was sufficiently certain of following Ancelotti to Stamford Bridge, that he had opened talks with Chelsea over personal terms, only for Milan to turn around at the last minute and declare their player not for sale.
"I have a very strong connection with Ancelotti so I was in touch with him when he went to Chelsea," the 33-year-old explained. "I'm still in touch with him now he's at Paris Saint-Germain.
"I had already started negotiating with the people at Chelsea but then finally Milan didn't let me go. That's why I stayed.
"Certainly it would have been a different experience that I'd have liked, especially when I was 30 years old. So why not? But unfortunately it didn't happen."
Now entering the twilight of his career, the Serie A star is enjoying his football in Turin, after joining Antonio Conte's Juventus side in 2011. But, even with two years still to run on his contract, taking him to 35, Pirlo remains open-minded about the possibility of one day featuring in the Premier League.
"Maybe, who knows? I don't know what might happen. You never know. I still have two years left with Juventus, this season and next," he added.
"I like English football a lot. There are plenty of very good teams. They are very aggressive so it's always entertaining to watch.
"It wouldn't be a problem for me fitting into that particular style because I've played with different players with different characteristics throughout my career."