Promoter Eddie Hearn is currently working on pitting Joshua against Parker for a unification bout next year.
And Whyte is currently in training for a fight against an unnamed opponent on February 3.
But he claims he would be willing to rematch Joshua if his negotiations with Parker fail to move past the current deadlock.
The two parties are struggling to come to terms over the financial rewards each fighter should get from their match-up.
So Whyte has chipped in to say he will try to avenge his 2015 defeat if it is not sorted soon.
“It’s either Parker or me, really,” Whyte told Sky Sports.
“As I’m older, I’m realising that this kind of fight – there is a lot of revenue and I bring a lot of value to the table as well.
“I’m happy to take the fight, but I’ve got to be compensated the right way, that’s all it is.”
And Hearn has indicated that he could pit Joshua against Whyte, if the former WBC heavyweight champion can regain a world title first.
“The first, is that Dillian could fight him next in March or April,” Hearn said.
“Two; he could fight Joshua in a unification fight. Dillian is on the verge.
“My aim for Dillian is to fight for the world heavyweight championship then fight Joshua in a unifier – that would be mega. We’ve got to get him a shot, which is difficult.”