The 20-year-old U.S. international Pulisic joined Chelsea from Borussia Dortmund in January for a reported fee of 58 million pounds but was immediately loaned back to the German club for the rest of the season.
With Hazard, 28, linked by British and Spanish media with a move to Real Madrid in the close season, Pulisic could be asked to fill the void and feels he is ready for the challenge.
Hazard has won two Premier League titles, the FA Cup, league Cup and Europa League crown in seven years at the club.
Asked if he could be as good as Hazard, Pulisic told Sky Sports: "Of course, I want to believe that I can be the best player I can possibly be.
"That's why I work so hard every day and why I thought it was necessary for me to take this next step in my career and to come here. I have so much more to learn as a player and am excited to see what the future holds.
"It's a great compliment (to be compared to Hazard), he's obviously much further along in his career than I am. He is an unbelievable player."
Pulisic, the most expensive American soccer player of all time, could be Chelsea's only new signing ahead of the 2019-20 campaign as they face a two-window transfer ban.
He has mostly played on the right wing for Dortmund this season but could be asked to move to the left flank or take up the number 10 role depending on Hazard's future at the club.
"I guess I have a similar style with an attacking and creative mindset like he does, he's very quick and shifty," Pulisic added.
"There's a lot to learn from him. It would be a great goal to do what he does. Everyone can see he is an unbelievable player and I would be honoured to play alongside him."
(Reporting by Hardik Vyas in Bengaluru; editing by Ken Ferris)
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