The 20-year-old signed a five-and-a-half year contract at Stamford Bridge in January to move from Borussia Dortmund in a £58million deal which saw him loaned back to the Bundesliga club for the rest of the campaign.
Hazard has been strongly linked with a move to Real Madrid and has just one year left on his existing contract, with Pulisic set to replace the Belgian if he leaves the Premier League outfit.
But the United States international aspires to emulate Hazard’s achievements at the club, regardless of whether the 28-year-old remains at Chelsea.
“It is incredible to see what Eden can do,” he told BBC Sport. “He is a guy to look up to and what I would love to become.
“It is definitely a goal. Any player would be dumb not to want to be in the same team as him.”
Speaking to the club’s official website, Pulisic added: “Eden is a fantastic player, we all know that and if I can get anywhere close to that I will be happy.
“He is a great player. I want to come in, be my own player, and do the best that I can do.”
Pulisic briefly moved to England as a child and had a stint at non-league side Brackley as a seven-year-old.
And the forward spoke about how those experiences helped push him to fulfil his dream of playing in Europe, and more notably in the Premier League.
“I just remember going to a few big games around the Premier League with my dad,” he added. “I remember coming to a Chelsea game and games at a few other Premier League clubs.
“I always wanted to play professionally, especially in Europe. And the Premier League was what I was able to watch growing up in the US, and it is always where I wanted to be.
“Now I just felt that it was the right step [to join Chelsea]. It was a great time in Dortmund but it was a feeling and I still have that.
“This is the biggest stage, it is incredible to come in and be in England and part of this league. If you want to prove yourself it is the greatest stage to be on.”
Provided by Press Association Sports
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