Joshua became a two-time world heavyweight champion by winning his rematch with Andy Ruiz Jr. on Saturday night, but immediately has Oleksandr Usyk (WBO) and Pulev (IBF) circling as his two mandatory challengers, Sky Sports News reported.
Asked how soon a decision would be made about Joshua's next fight, Hearn told Sky Sports, "It's going to have to be quite quickly, because obviously now the vultures will be out, as I would be. I don't blame them.
"I've got to speak to the IBF and the WBO and see who goes first. I think it sounds like it's the IBF, but we'll wait for confirmation of that. AJ will want to maintain the belts and if that's the case, I think it will be Pulev, and then Usyk.
"I think April or May, that's a realistic kind of date [for Joshua's next fight]."
Hearn added that the Tottenham Hotspur Stadium is in the running to host the fight, "We spoke to Spurs about hosting this fight (the rematch against Ruiz), which they were keen to do, but unfortunately the dates didn't work out. They would be keen to do it and it would be a nice stadium to do it in London."
WBO president Paco Valcarcel stated immediately after Joshua regained the belts that he would be obliged to defend against Usyk within six months. But, prior to Joshua's rematch with Ruiz Jr., the IBF told Sky Sports that they expected their mandatory challenger, Pulev, to receive his chance first.
"Ours has to come first," an IBF statement said.
"The organizations have agreed that the IBF mandatory would be next."
And Pulev's promoters Top Rank told Sky Sports, "Kubrat Pulev's next fight will be for the IBF world heavyweight title."
Bulgaria's Pulev, 38, has lost just one of 29 fights, against Wladimir Klitschko five years ago. He has beaten Derek Chisora and Hughie Fury since and was scheduled to fight Joshua in 2017 but withdrew injured.
Meanwhile Usyk, who became undisputed cruiserweight champion last year and won his heavyweight debut in October, plans to fight Chisora if, as expected, he misses out on immediately challenging Joshua.
Joshua, soon after regaining the IBF, WBA and WBO belts in Saudi Arabia, indicated his willingness to take on Usyk. They both won gold medals at the London Olympics.
"Let's rock and roll, mate. No problem," Joshua said about fighting Usyk.
Elsewhere in the heavyweight division, Deontay Wilder is expected to defend his WBC title against Tyson Fury in February.
Joshua said after his fight on Saturday night, "Oleksandr Usyk, Pulev, Ruiz, I don't want to mention the other guy's name, you know who they are, but when they're ready.
"I'd love to unite the belts [against Wilder], but I think me chasing him, same as in the fights, if I'm chasing the right hand, I'm chasing the right hook, it may come crashing down.
"I realize that chasing that fight wasn't playing into my benefit. I've just going to let the path take its course. I've got great people managing me. I've got a great team, and when the opportunity presents itself to become undisputed heavyweight champion of the world, you know me by now, I'll definitely step up and take the challenge."