Hazard is seen as one of the best players in the club’s history, helping the club to win six major trophies, including two Premier League titles, during his seven-year stay at Stamford Bridge.
The Belgian was sold to Real Madrid last summer, with Pulisic brought in from Borussia Dortmund to help fill the void.
The American experienced an injury-hit start to life in in London, but has been in excellent form since football’s restart and won a penalty during Saturday night’s 3-0 win over Watford, his tricky, direct style earning comparisons to his predecessor.
“Obviously, [Hazard] was an incredible player for Chelsea,” Pulisic told Sky Sports. “And he’s a world class player so I’m not trying to compare myself to him just yet.
“I’m just trying to be my own player and hopefully the fans like that guy!”
The win over the Hornets saw Frank Lampard’s side move back into the Premier League top four after they had been leapfrogged by Manchester United earlier in the day.
The three points could be crucial in an increasingly tight race for Europe, following the shock defeat to relegation-threatened West Ham in midweek.
"We needed that one today,” Pulisic added. “We came out with a lot of energy and we needed a huge result, especially after dropping points in the last game. There was a bit of extra energy because of that loss and we wanted to prove a point.
"[The top four race] going to be close and come down to the end. We are excited and confident we can do it."