The Belgium international was once again at his scintillating best for Chelsea last night, scoring two goals to help Antonio Conte’s side return to winning ways against West Brom.
Hazard’s future has been a hot topic in recent months with Real Madrid strongly linked with a big-money move in the summer.
That has ramped up pressure on the Blues to tie the 27-year-old down to a new deal, although his father recently claimed his son was holding out to see if the La Liga giants would make a move for him at the end of the season.
Hazard has remained relatively quiet on the issue, although he did shoot down his dad’s comments.
Chelsea return to action this weekend in their FA Cup fifth round tie against Hull before they face Barcelona in the Champions League next week.
Those two competitions remain Chelsea’s only real hope of silverware this season, but Carragher insists Chelsea can’t afford to drop out of the top four if they want to keep hold of Hazard.
“He is one of the top players in world football, there’s no doubt about that,” Carragher said on Sky Sports.
“The unfortunate thing when Chelsea are talking about getting into the top four tonight and Hazard said Chelsea are made to win trophies, this season they can still win the FA Cup and the Champions League, but if they don’t get into the top four, you would have to worry about him.
“I think every top club in world football would be looking at that situation if they didn’t get Champions League football.
“He is one of the strongest players in the Premier League. The world’s greatest ever players that we’ve seen, not just in the Premier League, are often flair players so as a defender, you think ‘I can leave one on them’ or something like that, but you can’t bully the best players.
“He’s exactly the same, and he has that strength where you can’t get the ball off them.”