The outspoken Fury has not hidden his desire to face Haye and on Sunday said a deal was 99% done.
Haye had been set to face Manuel Charr - his comeback fight from retirement - on June 29, but withdrew because of a hand injury and is now looking for a new opponent.
He claimed on Monday night Fury is not currently penned in but did say on Twitter: "For everyone asking if I'm fighting Fury. I currently have no agreement, or contract in place. But a fight later in the year would be fun."
Fury, who had asked Haye's trainer and manager, Adam Booth, on television on Saturday about making the fight, recently pulled out of a fight with unbeaten Bulgarian Kubrat Pulev, which was set to earn the winner a shot at current IBF champion Wladimir Klitschko.
The Charr scrap was set to be Haye's first since he beat Dereck Chisora in July last year - a fight which came about while he was in self-imposed retirement.
The Londoner has a long-term plan of dethroning the Klitschko brothers and a fight with Fury would not only allow him to move closer to becoming a mandatory challenger, but bring in good numbers on the till.