The F2004 carried Michael Schumacher to his seventh and final world championship in 2004, and the German won 13 of that season's 18 races with it. His teammate Rubens Barrichello added two further victories.
Shortly before the Tuscan GP, an example of the car was driven around Mugello by Michael's son Mick, as part of Ferrari's 1000th race celebrations.
The F2 racer drove the same car at last year's German GP meeting at Hockenheim, and in the past he's also demonstrated one of his father's Benetton's at Spa.
Vettel took time to take a close look at the car prior to the run, and he made the revelation about his interest in it in an interview with his former Red Bull Racing team mate Mark Webber, who raced for the Jaguar team that season.
Their conversation went as follows:
Vettel: "This is my favourite car. Did you race [against] this car?
Webber: "I think I hit this car once in Turkey with Michael, he wasn't too happy with me. But when I see that car I just think of sheer performance, and Michael on top of things of course. It was extraordinary times, wasn't it?"
Vettel: "I was just saying, if you look to our cars, our cars are so much bigger nowadays. Obviously we've got a lot more downforce, but this car is 160-170kgs lighter than ours, so big difference."
Webber: "You've been adding to your collection recently. Do you have any cars of this generation?"
Vettel: "No, there was that one, not that exact one, but the same year up for sale, but it was way too expensive."
Webber: "Come on Seb!"
Vettel: "It was! It's an incredible car. You'll hear it later."
Vettel's current teammate Charles Leclerc, who turned seven in 2004, also took time out from his race preparations to look at the car.
"It looks crazy, it looks very, very nice," said the Monegasque driver. "But mostly it sounds nice compared to what we have now. It's part of Ferrari's history, a very special part of Ferrari's history, and it looks beautiful.
"I had the chance to drive once the 2003 car, never the 2004, but I hope in the future I'll have the opportunity to drive one of those."