Haye, who lost his WBA heavyweight title to Vitali's younger brother Wladimir in Hamburg last year, fought fellow Briton Dereck Chisora in July under a licence provided by the Luxembourg Boxing Federation.
Chisora's British licence was withdrawn after the pair's infamous brawl in February.
Haye, now 31, was officially retired when he and Chisora fought in the press conference following the latter's defeat by Vitali Klitschko.
And the British Boxing Board of Control warned that anyone involved when Haye and Chisora fought at Upton Park in London with licences from Luxembourg would "wholly undermine the authority" of the board.
But Bermondsey boxer Haye now wants to fight under the BBBoC again.
"I'd like to thank the Luxembourg Boxing Federation for licensing me ahead of my July bout with Dereck Chisora in London, but I no longer require that licence," Haye told the South London Press.
"It's been well-publicised already, but the reason I applied for a license from the Luxembourg Boxing Federation was because my opponent, Dereck Chisora, had seen his British licence withdrawn.
"The only way we were able to deliver the fight the public wanted, when they wanted it, was to both apply for foreign licences, as arranged by Chisora's promoter.
"In an ideal world, though, I'd now like to box on with a British licence. I'm a British boxer, I have never had any issues with the board and, should a fight with Vitali Klitschko happen, I'd be keen to have the British Boxing Board of Control in my corner, simply because they are so experienced and are the best at what they do."
Haye also laid down a challenge to Vitali Klitschko, seemingly hoping to ignite the 41-year-old's desire for a bout, despite the champion's move to stand for election to the Ukrainian parliament in October following his defeat of Manuel Charr earlier this month.
Haye said: "My aim is to get Vitali in a ring next year, after his election campaign has failed, and bring his WBC world title back to Britain.
"This is the only fight that interests me at heavyweight, and the WBC world heavyweight title is the one belt I'm desperate to win before I retire for good."