"It wasn't my idea and that just came across my desk. But some people say that," Higgins told Martin Devlin on Radio Sport.
"I don't think Anthony Joshua does steroids. I think he trains very hard to the point of boring. I don't know why [Parker said it].
"The advice from myself will be to drop it and stick to the things we know."
Parker, whose title unification fight against Joshua has been confirmed for April 1 (NZ time) in Cardiff, told the Radio Sport Breakast show that being called the king of pies by the Joshua camp didn't worry him.
''They call me the king of pies but I call him the king of steroids. Who knows, if you are that big and that musclelly there's something wrong.
''I have heard word; I have looked at him and I have seen. He has been very close with Klitschko ... he has been a reigning champion for a long time.
"So I don't know ... it may be true maybe not."
The fight was confirmed overnight by Joshua's promoter Eddie Hearn, who tweeted it would take place at Principality Stadium, a venue more famous for rugby internationals.