Ducati joined the MotoGP grid in 2003 and in 2007 celebrated its first world title with Stoner at the helm.
When Stoner left Ducati at the end of 2010, the Italian marque slumped down the order and wouldn’t win another grand prix until 2016, while it wouldn’t be until 2022 that it crowned a world champion for a second time.
Bagnaia overcame a 91-point deficit midway through the 2022 season to end Ducati’s 15-year wait for another title at the final round in Valencia last November.
Speaking exclusively to Autosport, Bagnaia says the comparisons between himself and Stoner are hard to comprehend for the Italian.
“It’s very difficult of me to see my name next to Casey’s,” Bagnaia said.
“When you’re little and you see your idols, you think it’s impossible to reach what they mean to you.
“It’s a bit like school when I was little and looked up to my elders. When I was a senior I didn’t see myself as different from what I was before.
“I know I won the title with Ducati like Casey did, and I won the record for consecutive [race] wins [with four in a row]. But I don’t see myself as him.”
Bagnaia says he has always had a deep love for Ducati and wants to become associated with the brand in the same way Valentino Rossi and Yamaha are linked.
“Since I was a child I’ve been one of the biggest fans of Ducati ever,” Bagnaia added.
“I’d like my name to be identified even more with Ducati. It’s a bit like Marc [Marquez] and Honda, or Valentino in the case of Yamaha.”
Heading into this weekend’s French Grand Prix at Le Mans – which will mark the 1000th world championship event – Bagnaia leads the standings by 22 points after taking victory at the Spanish Grand Prix.
Ducati has won three of the first four grands prix in 2023, with Bagnaia taking the spoils in Portugal and at Jerez, with VR46 rider Marco Bezzecchi winning in Argentina.