The Belgium captain has enjoyed a sensational start to the season and already has eight goals across all competitions.
His form has been crucial in helping Chelsea maintain an unbeaten top-flight record to join Manchester City and Liverpool on 20 points at the top of the Premier League table, while he also knocked the latter out of the Carabao Cup.
But Hazard’s performances will undoubtedly have caught attention of those in the Spanish capital, with the 27-year-old having been tipped to move to the Bernabeu in the summer after Cristiano Ronaldo’s big-money departure.
Hazard stayed but has thus far refused to sign a new contract with the Blues’ offer of a club-record £300,000-a-week extension even failing on deaf ears.
The forward once again hinted at a desire to move to the Spanish heavyweights this week as he hinted that playing for Real Madrid is something he has long been “dreaming about” as he declared: “We will see. We will talk about my future soon.”
But having been such a catalyst for Maurizio Sarri’s strong start to life as a manager at Stamford Bridge, having yet to lose any of their 11 games across all competitions, Barkley is keen for Hazard to sign a new deal and remain at the club.
And the England midfielder – who is enjoying his best form for several years under Sarri – hailed the impact of training and playing alongside someone of Hazard’s ability.
“It’s important,” Barkley said on keeping Hazard.
“He’s been at Chelsea for a long time now and he’s achieved so much. I can’t speak for Eden, he knows in his mind what he wants.
“But I’d love to play with him for many more years ahead. He’s inspirational, a magnificent player.
“You can see how he’s started the season and the World Cup that he had, you don’t get many players like him. He’s capable of magic at any moment.
“Playing with world-class players is always going to improve me, and to play with them, to train with them on a day to day basis, you see the speed of thought, you see how much enjoyment they have in football and it has a big effect on yourself.”
Hazard actually had huge praise for Barkley’s performance in their 3-0 win over Southampton at the weekend and enthused about the former Everton trainee’s potential.
“He [Barkley] played a fantastic game, and it is not just because he scored a goal or that he made an assist,” Hazard said.
“You can see on the pitch that he is very strong. He had some bad moments in the last year or two years with injury but I think he can reach a fantastic level because he is a fantastic player.
“I remember watching him at Everton. He is still young so I think he is a good player for the future with Chelsea.
“If you give Ross the freedom to play and the confidence on the pitch, he can be one of the best in the world in midfield.
“He is strong, he is powerful, he can dribble, he is clever, he can shoot, he can score and he can make assists.
“If he has players around him to help him to play, he can be one of the best.”