Wilder and Joshua appear on a collision course and are expected to fight at some point in the next 18 months.
However, negotiations are understood to have been difficult between the two camps with the purse split already proving a stumbling block in making the fight.
And now Express Sport understands that Wilder could snub the Joshua vs Parker fight on March 31, which will see the two men compete for the WBA, IBF and WBO heavyweight world titles.
WBC champion Wilder holds the only other belt and is understood to be considering a U-turn on his plans for Easter weekend, a move that would deal a blow to efforts to get him in the ring with Joshua.
Just three weeks ago, Wilder first announced that he would head to the Principality Stadium for the bout, a promise on which he is now appears to ready to renege.
“I am looking forward to Cardiff, I have never been there,” Wilder said last month.
“I have a lot of friends in the UK. I am going to enjoy myself and look forward to fighting the winner – if they are up for the test.
“I’ll defend my title anywhere in the world. I believe in giving people the chance to stay in their own home.”
Wilder is unbeaten in 40 professional fights and has held seven successful defences of his WBC crown.
But his most recent fight was by far his most impressive as the American overcame the unbeaten Luis Ortiz by 10th-round knockout, having been rocked during the middle rounds.
And if Joshua overcomes WBO champ Parker in Cardiff, the pair will be on course for a bout that will unify the heavyweight division.
However, the Brit warned Wilder that his overinflated self-worth – he demanded £5million from promoter Eddie Hearn to fight No 1 challenger Dillian Whyte – could see him talk himself out of a unification bout.
“If he was serious about the fight, we’d do serious negotiation. If not, stop hooting and hollering because we’ll just freeze him out,” Joshua said.
“We’re in a position where I’ve still got great top-10 challengers I can compete with.
“He’s in a position where the broadcasters ain’t interested in [Wilder against] Joe Bloggs anymore.
“I know where I am going with my career. If he wants to be a part of this and jump on the train and come to the UK, he has to be realistic and stop living the fantasy.
“That is all we are saying, be realistic in negotiations.”
Wilder’s representatives failed to respond to request for comment on his presence at Joshua vs Parker.
