Brook and Khan open talks over 2013 meeting
Brook's promoter, Eddie Hearn, believes the contest is almost "inevitable", saying that he hopes by the time the fight is made Brook will be able to put his IBF welterweight world title on the line.
Hearn revealed that negotiations between the two camps began after Khan's loss to Danny Garcia earlier in the year, but stepped up a notch following an explosive appearance together on a boxing television show.
"I think this fight is inevitable, it's too big to be ignored," Hearn told Sky Sports. "Both fighters want the fight. Amir Khan thinks he can take care of Kell Brook, and Kell thinks he can also take care of business.
"The first indications from their team is that they really want this fight. This is one of those super-fights that could take British boxing to a new level. These are the fights we want to take."
Each man has challenges in their way before the fight can happen, however. Brook is preparing for a fight against Hector Saldivia to decide who will be the mandatory challenger for the IBF welterweight strap, and then aims to fight for that title in the New Year.
Khan, meanwhile, is looking to get his career back on track with a comeback win against Carlos Molina at light-welterweight in December - but even a comprehensive victory might leave him with few attractive options within the division.
If the Bolton fighter then finally made his long-expected step up to welterweight, a chance to fight for Brook's newly-acquired IBF title may be too good an opportunity to turn down.
"Amir's got to look at his own career and say, 'Well, where am I going from here?'" Hearn noted. "The Brook fight might be the most attractive option open to him after that December fight against Molina.
"I think this fight is definitely one that could be made in 2013."
Whenever the fight does get made, Hearn is confident Brook will triumph. "Amir Khan has been knocked out at lightweight, knocked out at light-welterweight - and we think if he moves up to welterweight as well he'll get knocked out there too," Hearn said.
"I think when people see the new, improved Kell Brook he'll be a strong, strong favourite to beat Amir Khan."