"One side of me says, with all due respect, that he is irrelevant because he is not fighting, he is not active", added Joshua.
Wilder destroys Stiverne in NY.
If Joshua's a strong champion, a true champion, you guys in England should smoke him out, make him fight.
"An American guy in China who does have credentials and money and they wanted to look at staging a heavyweight title fight out of China - Parker v Zhang Zhilei". Present him with an offer, and see how they feel about that offer. "If you want to stay at home like a little girl, this king has no problem travelling to knock out the champion". "If Wilder's not making an offer, we'll do it on my terms".
"I'm ready to dethrone you, I will be heavyweight champion of the world, I will defeat you".
Joshua also said that he would preferably have an arrangement in place with Wilder by Christmas, so that he can begin his fight preparations in the first week of January.
"That only goes to the champions: Deontay Wilder and Joseph Parker".
Wilder, whose one-round demolition of Bermane Stiverne in NY on Saturday took his blemish-free record to 38 knock-outs in 39 wins, delivered a taunting message on social media, declaring he would beat Joshua in his British "safe haven".
And the chances of a fight happening next year appears to be even more likely now, after the WBC champion called out his rival. "It's the same situation to both of them". "There has never been an offer".
Another fighter seeking a fight with Joshua is 25-year-old Parker, who has won all 24 of his professional contests - 18 inside the distance - although he needed a controversial majority points decision to beat Hughie Fury, cousin of Tyson, in September. He wants something better for his fighter.
"What we then have to do - which Eddie's doing - is fly out to the United States to make time. When he is back we will get the ball rolling, until then it's not relevant to me".
Joshua's fight with Takam in Cardiff was a huge success and broke Muhammad Ali's longstanding record for the biggest indoor boxing crowd.