The 28-year-old, who holds the WBA and IBF versions of the crown, goes into the March 31 fight in Cardiff with a perfect 20-fight, 20-knock-out record.
WBO champion Parker is unbeaten in 24, with 18 knockouts, and he and his camp have brought attention to past occasions where Joshua was knocked down in the ring as amateur and professional.
There has been talk of Joshua having a 'glass chin', with Parker using the Twitter hashtag #neverbeendropped to emphasise his own ring record.
Appearing at his first pre-fight news conference with Parker in London on Tuesday, however, Joshua said it would take 'more than a human' to beat him and accused his opponent of a PR stunt.
"When you talk about myself getting dropped and what you done, it's a marketability strategy," he added.
"The rumours that you have heard, they're all fake news. Hand on my heart. PR, whatever you want to use it for, is between you and your camp."
Parker recognised he had a big challenge but remained confident.
"I've watched him for a long time. I know he's watched me. I know his strengths, I know that he knows mine. I know his weaknesses and he thinks he knows my weaknesses," he told reporters.
"And I'm hoping to catch him on the chin and knock him out."
The winner of the fight will take a step towards becoming the first undisputed heavyweight champion since Lennox Lewis in 1999-2000.
American Deontay Wilder holds the WBC belt in the heavyweight division.
(Reporting by Alan Baldwin, editing by Christian Radnedge)
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