His manager, Maurizio Sarri now wants Hazard to score more goals but Chelsea's chief playmaker has a different idea of what his role should be.
Hazard has netted 12 times in the Premier League this season, a tally which is just four short of his best ever return for the Blues — he scored 16 goals in the 2016-17 campaign.
But despite being in relatively good form in front of goal, Hazard claims that manager Maurizio Sarri is demanding much more.
Hazard has also provided 10 assists in his first 24 League games this term and he told The Times: 'I'm not at all selfish.
'The way I am can be a weakness to be the best player in the world. Managers like [Jose] Mourinho, [Antonio] Conte, now with Sarri want me to score 40, 50 goals a season but can I do that? I'm not sure.
'Maybe they think I can, but I know myself and I don't think I can. But I will try.
'I like to be 'the star' but I like also when I can pass the ball to another for him to score, and it is not just about me. It's about everyone. My target is to help the team to win something.'Hazard has won two Premier League titles in six and a half years at Stamford Bridge, also lifting the League Cup, FA Cup and Europa League.
Many believe this season may be Hazard's last in London, with Real Madrid linked with a summer move for the 28-year-old Belgium captain.
Hazard could ultimately be seduced by Real's ambition but Chelsea showed in January that they are also committed to improvement by bringing in Argentina striker Gonzalo Higuain, 31.
Higuain and Hazard played together for the first time in a dreadful 4-0 loss to Bournemouth. But they linked up to good effect last weekend when Chelsea thrashed Huddersfield 5-0 in what was arguably the team's best performance since Sarri took charge last summer.
Discussing 60-year-old Sarri, Hazard added: 'I like this kind of football. Sarri is a great manager. He's an old man but the way he thinks is the same way I think about football. When we have the ball, we have a lot of freedom, not just me but the striker and the right [winger] Willian or Pedro, so we can move a lot.
'I've only played two games with Higuain and I know we can do something great together, not only with him but also with the other strikers, the other winger.
'Chelsea is not about Higuain and Hazard, it is about 25 players. But Higuain is a fantastic striker.'
Next up for Hazard, Higuain and Co is a trip to Manchester City on Sunday.