"I think it's not nice, I don't really respect it and I have no time for it," said the IBF and WBA champion. "What's he trying? Be the big bully? Demonise everything I have done?
"In Formula One, golf, tennis, rugby, they are very classy people, respectable about their peers. Then you have people like Joseph Parker holding a press conference talking about everything he thinks I am."
Should the fight happen, the winner could then face WBC title holder Deontay Wilder in a bout which could unify all four major titles in the heavyweight division.
Joshua beat Wladimir Klitschko to claim the WBA title in April, and followed that success with victory over Carlos Takam in October.
"This is the first time in my career where the talk has been about money," added Joshua. "That's what's holding it up. With Klitschko, it wasn't about the money, it was about getting the fight together for the belts. With Parker, it's a different story, and Wilder.
"No disrespect for them, they have their reasons, but I feel like the fans are not getting what they want.
"It would have been great to have it pencilled in now but it will happen in the future once they come to their senses. What they are offering is nothing, and what we are offering is 10 times better than what they can bring up themselves," said Joshua.