Hazard, 28, appears poised to move to the Bernabeu with the Blues reportedly willing to sell him for £87million this summer.
Chelsea acted in January by signing Pulisic from Borussia Dortmund for next season in a deal thought to be in the region of £58m.
It’s been suggested the American international was bought in preparation for Hazard’s departure but Pulisic maintains some hope that he will play alongside Chelsea’s star player.
Speaking to talkSPORT’s James Savundra in London, Pulisic said: “I think anyone can play alongside him [Hazard], he’s a great player. It would be great to play with him absolutely. I’m going to come in and give it my best.
“I’ve been able to see on the TV what he’s done and he’s obviously a great player.”
When the Pulisic transfer was confirmed in January, Chelsea boss Maurizio Sarri claimed to have no knowledge of the deal until it was announced publicly by the club.
But Sarri’s 4-3-3 system should cater well to winger Pulisic’s strengths and the 20-year-old believes his and the Italian’s styles are a ‘great fit’.
Pulisic added: “Chelsea was a place I just couldn’t refuse. I watched Chelsea growing up and saw them have success in Europe and I always think of the team as champions.
“I’ve always wanted to play in the Premier League and it feels like the perfect spot for me.
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“I want to come in and make an impact as soon as I can. I’m going to work as hard as I can from day one to make sure I can do that.
“I think I’m going to fit in very well [into Sarri’s system]. It’s a very attacking system which will work great for me, on the wings and in great attacking positions. I think it’s a great fit.”
Pulisic arrives at Stamford Bridge knowing he will play Champions League football next season following Chelsea’s third-place finish in the Premier League last season.
There were a lot of negative moments in the 2018/19 campaign and Chelsea finished 26 points off title winners Manchester City and 25 points off runners-up Liverpool.
However, Pulisic believes there’s no reason why his new club can’t challenge for the crown next season.
He said: “People can say what they want but Chelsea had a great end to the season. They’re in the Europa League final and they finished in the Champions League spots for next season.