Hearn told Sky Sports discussions had taken place with Paul’s representatives, but stressed a deal wasn't yet close and accused some reports of "jumping the gun”.
He said Joshua would only entertain a fully-fledged professional bout under standard Queensberry rules, with 10-ounce gloves and a mutually agreed weight. Paul typically fights at cruiserweight, but the proposal would likely be sanctioned as a heavyweight bout.
An offer has been received from Paul’s camp, though Hearn questioned whether the American influencer would accept the demands of facing a former world champion in a regulated contest.
Joshua had been preparing for an eight-round fight later this year, initially pencilled in for an undercard slot, but the Paul proposal is thought to be "50 times" more lucrative, according to Hearn.
The promoter framed the idea as a short-term commercial opportunity rather than a meaningful step in Joshua’s career, stressing that the British boxer's focus remains on major heavyweight bouts.
"So if we do run out, and just wipe out Jake Paul before Christmas, and make, I don't know, £50m or £60m... sweet as a nut," said Hearn. "If not, we won't do it, and we'll wait until February.
"The best thing to be in this situation is honest, we ain't turning this down. The serious stuff is very much the focus of what we're doing, but this would be something small in between."
Talks continue over a long-planned meeting with Tyson Fury, targeted for 2026 with Saudi backing.