The social media star has been pushing for a bout against the former heavyweight world champion and his representative Nakisa Bidarian is in talks with Joshua's promoter Eddie Hearn about a possible fight.
Bidarian told Sky Sports News: "I think the fight can absolutely happen. I'm looking at it as Jake versus Joshua, which is quite biblical, and it's quite impactful in many ways.
"I think size-wise, we can get comfortable with it, and I think experience-wise, Jake is learning very fast and growing, and Joshua is a little long in the tooth. So it could be a very interesting matchup, and we're actively discussing it with Matchroom.
"I think we're looking at it happening at the start of 2026. It's public that AJ was taking a little time away, I think he had a little surgery. So once he's ready, and once Jake is ready, we're going to squarely focus on that.
"It's a fight that Jake wants to do, and that's a discussion we've had at length, and he feels very confident about where he is in his career and his chances of upsetting Anthony Joshua."
Observers have expressed doubt as to whether Paul - who defeated boxing legend Mike Tyson last year - is capable of taking on an active heavyweight but his promoter insists that the star wouldn't accept the fight if he wasn't ready for it.
Bidarian said: "Power is obviously the last thing to go. So obviously, AJ has a ton of power, and he's still fairly young. Mike Tyson - much more vicious of a knockout artist than Anthony Joshua - that was a risk Jake was willing to take.
"Francis Ngannou, amazing MMA fighter, very powerful man, but not an experienced boxer, right? He is a lot less experienced than Jake Paul. So if people were comfortable with Francis getting in there with AJ, Jake, who is now 13 fights in, plus one amateur fight, then we are comfortable with this."
The promoter has suggested that Wembley Stadium is a possible venue for the blockbuster fight.
He said: "Wembley's definitely a possibility. Jake said he'd like to do it there. He likes the idea of going in and hearing 90,000 people booing him!"
