The New Zealander has returned to Britain for Saturday’s fight with Whyte at The O2, live on Sky Sports Box Office, just a few months after losing his WBO heavyweight belt in a points loss to Joshua at Cardiff in March.
Joshua makes his next world title defence against Alexander Povetkin at Wembley on September 22, live on Sky Sports Box Office, with another bout lined up at the national stadium for April 13, and Higgins says Parker could be a worthy replacement if Deontay Wilder does not take that date.
“The knockout would be ideal and it would really put us in pole position to legitimately demand a rematch from Joshua,” Higgins told Sky Sports.
“We want Anthony Joshua next, and we would be demanding the rematch.
“Joseph Parker is only focused on Dillian Whyte, but should he beat Dillian Whyte then he’ll probably be the most prominent heavyweight currently after Joshua-Wilder.
“We think on a different stage, on a different night, with a different referee, and Joseph learning from his mistakes, and putting real pressure on, we think Joshua is absolutely beatable.
“He’s a human being. We don’t think he’s near the top echelon of all-time great heavyweights. He’s nowhere near that yet. He’s got a lot more to prove.”
Parker agreed a unification clash with Joshua after lengthy negotiations and Higgins believes Wilder could miss out on a massive unification fight for all the world titles, unless he lowers his terms.
He said: “My message to Deontay Wilder – ‘Pull your head in, stop being greedy, and make the Joshua fight, otherwise the winner of Parker-Whyte is going to take your slot and you’re going to sit on the shelf for another six months, and you might lose the opportunity all together.’
“[Advisors] Al Haymon, Shelly Finkel, and Deontay Wilder, you’re coming under more time pressure.
“Joshua is the A-side commercially, and they’ve got options, and they could quite easily put the winner of Parker-Whyte into Wembley and still sell it out, until you stop trying to overreach, and take more money off the table than what you’ve earned.”
Parker admits he is eager to avenge his sole defeat to Joshua as he wants to prove himself against the best fighters in the top division.
“If all goes well, we get through Dillian Whyte, which we think we can, listen bring on anyone,” he told Sky Sports.
“I want a rematch with Joshua, maybe with a better ref. Wilder, anyone, Tyson Fury. I just want to fight the best in the world to test myself.”
Watch Dillian Whyte vs Joseph Parker with Katie Taylor, Dereck Chisora, Joshua Buatsi, Conor Benn and more the undercard, live on Sky Sports Box Office, from The O2, Saturday, July 28.