Real Madrid are believed to be keeping a close eye on the 27-year-old's situation and he has yet to open up on his long-term plans.
The attacker's contract is due to expire in 2020, but Chelsea seemingly have different priorities at this stage, with manager Antonio Conte set to make way for former Napoli boss Maurizio Sarri .
Nevertheless, Lampard feels Chelsea should do everything within their powers to hold on to Hazard, even if he was reluctant to touch on the financial side of the matter.
"I do not want to say Chelsea should pay him whatever he wants, because I do not know the numbers," Lampard exclusively told Goal during the BBC Media Day.
"But in terms of the player, if you are a Chelsea fan, you want Hazard to stay. He is a world-class player, without a doubt. He is a talisman of the club, because he is magic, when a game is tied, he normally steps up to change things. He can create something out of nothing and I think he is fantastic.
"If you want to keep moving forward, you need to keep players like Hazard if you can and then add to it around him.
"I obviously hope he stays, but in terms of pay, do not ask me… That is for them to deal with."
Hazard netted 12 goals in 34 Premier League appearances this term, but was unable to guide Chelsea to Champions League qualification as they had to settle for fifth place in the table.
He ended the season on a high, though, as he scored the winner in the 1-0 FA Cup final win over Manchester United.
The BBC will provide extensive coverage of World Cup 2018 across TV, radio and online from June 14.