Bolton's Khan, 30, said earlier this year that Sheffield's Brook, 30, is not a big enough name for him to fight.
But on Wednesday, Khan suggested on social media he would be the next fighter "to smash Kell Brook's face", while Brook responded by saying he wants to "send him back to sleep".
Hearn told BBC Sport: "There's a good chance of it [the bout] happening."
The promoter added: "Amir wants it to happen, so does Kell. We want to put a fight on for the fans."
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Both boxers lost in their last fights after moving up to middleweight, with Brook being stopped in the fifth round by Gennady Golovkin, while Khan was knocked out in the sixth by Saul 'Canelo' Alvarez.
Brook and Khan said after their fights that they would not fight at that weight classification again and it is not yet known whether champion Brook's IBF welterweight title would be on the line.
Hearn said the all-British fight could take place "up north in Manchester Arena or Old Trafford".
"Kell has proved himself. He beat Shawn Porter and had a good fight with Golovkin. The time is right," added Hearn.
Kell Brook and Amir Khan "are in talks" to stage a fight in May 2017, according to Brook's promoter Eddie Hearn.