AJ, 35, has been out of action for the past 12 months after sustaining an elbow injury during his fight with Daniel Dubois, 28, and Nelson, 58, has argued Joshua should consider throwing in the towel for good.
During an appearance on talkBOXING podcast, the former cruiserweight world champion said: “I think for Anthony Joshua, coming from a place of love, I think Anthony Joshua's got nothing else to prove in this game.
"He should rather walk away than hang about and wait for someone to turn him over.
“It's either him and Tyson Fury, which we're all sick of the is it happening or isn't it happening? Or just walk out of it.
“He's a very comfortable, wealthy man.”
Jake Paul, 28, recently called out Joshua, and AJ’s promoter Eddie Hearn, 46, seems to have entertained the fight, though Nelson doesn’t think such a match-up will actually go ahead.
He said: “I don't think Jake Paul was ever going to happen. I don't think it was ever going to happen, even when Jake Paul was shouting it out and Eddie propped it up a bit, by the way.
“It was never, ever going to happen.”
Hearn recently said he wouldn’t consider a fight between Paul and Joshua unless The Problem Child beat Gervonta Davis, 30, in their exhibition bout next month.
He told Sky Sports: “They’ve come on to me and said, ‘We want to make that fight [with AJ].’ I said, ‘I can't make that fight until you've fought Gervonta Davis in this exhibition.’
“If you get chinned by Gervonta Davis, don't think you're fighting Anthony Joshua, it's ridiculous. So we'd rather they didn't take that fight if we're going to make the [Joshua] fight.”
Instead, Hearn revealed he has a list of roughly 10 boxers that he would be interested in seeing Joshua share the ring with next - including Tony Yoka, Martin Bakole and Efe Ajagba.
Speaking with iFK TV, he said of 33-year-old Yoka: “The name comes up all the time, I don't know where it came from, but in a pool of 10 fighters, yes, he is in that pool.
“The first fight back is not going to be [Tyson] Fury, [Oleksandr] Usyk, [Daniel] Dubois, [Joseph] Parker, or Moses [Itauma].
“It's going to be a proper fight, but it is not going to be against the top five. It might not even be against someone in the top seven or eight.
“But it all depends on the plan. When you are planning something like this, you aren't just going ‘Oh, who is he fighting first?’
“We're planning out probably the next three fights, and who we fight in fight three may even determine what we do in fights one and two.”
