"Last season, I scored a lot of goals and maybe this season I can make a lot more passes forward because Costa is one of the best and he can score," said Hazard. "It's my job to score, but it's also my job to make assists as well."
Hazard was Chelsea's leading scorer with 14 Premier League goals, including four penalties, last season, but Costa's arrival - with four goals in his first three outings - has changed the dynamic in Chelsea's attacking play, easing the pressure on the Belgian.
"The new players have settled in very good. I enjoy playing with the best players in the squad and I'm very happy," he was quoted telling Chelsea TV by the London Evening Standard. "We have a very competitive team and we want more than last season.
"Last season we played good but we didn't win any trophies so we want more. We can win four trophies and I hope we can compete in the two cups, the Premier League and Champions League for a long time throughout the year.
"Costa can score every game and Cesc is one of the best midfielders in the world. Cesc can score as well and make good assists."
Hazard also revealed that he has a close relationship with Spanish left-back Cesar Azpilicueta, who has kept new signing Brazilian Filipe Luis out of the team.
"I have Azpi behind me and he helps me when I attack or have to defend. Off the pitch, we are very close friends because he can speak French and understands everything.
"It is important for me to play with him because I know how he plays... I think he can reach the level of being one of the best right or left backs in the world."
Table-topping Chelsea, who impressed with a 6-3 win at Everton in their last outing, meet second-placed Swansea at Stamford Bridge on Saturday with both Hazard and Costa expected to recover from slight injuries and play.
(Reporting by Tim Collings; editing by Sudipto Ganguly)
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