The 36-year-old former two-time unified heavyweight champion will face The Problem Child, 28, at the Kaseya Center in Miami, Florida on 19 December, and Warren has argued the stakes could not be higher.
Speaking to Sky Sports, Warren said: “If he looks bad against Jake Paul, when you consider the experience he has and what Jake Paul’s got, then I think he should turn it in.
“I come from a traditional background in boxing and the bottom line of it - you think a good big ’un will beat a good little ’un. Well, AJ didn’t look so good in his last fight, he got absolutely taken apart by Daniel Dubois.”
Warren acknowledged that while Paul has limited experience -“he’s had 13 fights, that’s it” - the risks remain huge for Joshua.
The promoter described the bout as “a massive, massive step up” for The Problem, but warned there’s little margin for error for AJ.
He said: “It's a massive, massive step up for him, it's a massive step up.
“Fighting a natural heavyweight, a big guy, a two-time heavyweight world champion, Olympic gold medallist, all that, it's a massive, massive first step up and he'll go in as a big underdog, a big, big underdog.
“But everyone will be watching it.”
Warren added the fight could be like “a car crash”, but insisted people “will buy into it, and they'll watch it and it'll do big, big numbers” for Netflix - who will be streaming the blockbuster bout live.
Elsewhere in the interview, Warren said Tyson Fury, 37, is close to announcing his next steps after initially retiring from boxing following his loss to Oleksandr Usyk, 38, last December.
The promoter said: “If he's going to come back he'll make his decision and he'll do that fairly soon I think if he's going to do it.
“He's indicated he wants to. It's not just whether he wants to. It's also the finances and what the deal would be. Let's see what happens.”