The striker has gone AWOL in Brazil this summer after being told by Antonio Conte he is not in his future plans.
Costa subsequently pushed for a move to former club Atletico Madrid.
But no agreement was reached before the transfer window shut, leaving the Blues star in limbo.
Starsport understands Costa is set to return to west London for peace talks, as he cannot leave until January.
Hazard may get his wish as a result, with both eager to feature at the 2018 World Cup too.
“Diego and I have been playing together for three years,” Hazard told Marca.
“We won everything together except the Champions League.
“It is a pleasure to play with him: he is a top player and a top person.
“I would like to see him back, but I do not make the decisions.
“I hope we can find a solution and see him on the field soon.”
Alvaro Morata was brought in this summer from Real Madrid for a club-record £70m to replace Costa.
And on his new Chelsea team-mate, Hazard added: “I’ve never played with him and I’m looking forward to it.
“He is still very young, but he has won many titles with Juve and Madrid, so he has a lot of experience.
“We need this type of player, able to score many goals, and Alvaro can do it. We are happy with him.
“He is a good boy, talkative, even in English. We are looking forward to playing together.”
More Breaking News:
Ross Barkley refused Chelsea move because Antonio Conte turned his phone off, claims Joey Barton
Ross Barkley refused to sign for Chelsea because he could not speak to Antonio Conte on deadline day as the Italian had his phone switched off, according to Joey Barton.
Everton agreed a £35m fee for the England star before Barkley decided against the move.
Toffees majority shareholder Farhad Moshiri even claimed he had started his medical – a claim later denied by the injured player.
Now Barton has claimed the real reason for the move to fall through was Barkley had wanted to speak to Conte about his future role before signing – but could not get through.
The former Manchester City and Newcastle star told talkSPORT: “I heard a really interesting thing about what happened with the Ross Barkley transfer. Conte turned his phone off and Barkley’s representatives were trying to contact him.
“He wanted to say: ‘Look, where am I going to play’, and Conte turned his phone off. That is why Barkley got cold feet and never signed.
“He thought: ‘Well, if the manager isn’t answering the phone to me he clearly doesn’t want me’, and that is why he went back to Everton.”
The collapse of the Barkley deal followed failed bids to sign Romelu Lukaku and Alex Oxlade-Chamberlain.
Chelsea and Tottenham are expected to go back in for Barkley in January. He is out of contract next summer.