Pulisic, 21, has scored three goals in his last five league games and helped Chelsea remain in pole position for a place in the Champions League next season.
Hazard won two league titles at Stamford Bridge before moving to Real Madrid last summer and Pulisic said he is focusing on making his own impact on the club.
When asked about Hazard, Pulisic told Sky Sports: "He's an unbelievable player. It's pretty obvious what he accomplished at this club and I'm not trying to compare myself to that.
"What's important for me now is winning games and having an impact for my team.
"I'm really happy I can do that as of recent and my style is always going to continue to be that very attacking-minded and creative kind of player. I'm happy I can help the team any way I can."
"I'm excited to work with them," he added. "It's fun to play with good players, it's easy to play with them and those are two guys we know that are really talented guys so I'm really looking forward to it.
"You can see this year that those two, especially Liverpool, have been just so consistent and dominant and that's right where we want to be.
"We want to continue to win trophies, that's always a goal. We want to continue to be a strong team, contending for that Premier League title."
Chelsea return to league action on Saturday with a trip to Sheffield United.
Lampard told a news conference on Friday that midfielder Billy Gilmour will be out of action for up to four months after a knee operation.