Parker's promoter David Higgins said Joshua is rattled and warned that Tuesday's pre-fight news conference will start without Joshua if he arrives late, as he has done in the past.
While Joshua will put his WBA and IBF titles on the line, Parker will be defending his WBO when the two come to blows at the Cardiff Principality Stadium next Saturday.
Tune into talkSPORT for LIVE and EXCLUSIVE coverage of Joshua v Parker - DETAILS HERE!
Despite being unbeaten in 24 fights as a pro, questions remain over whether Parker can deal with the power of Joshua, who is taller and will be heavier on the night.
"[Joshua's trainer] Rob McCracken said to me, "Once you get into the ring with Joshua and you get hit by him with 10oz gloves on, everything changes", and he's right".
March for Our Lives
Mike spent hours replying in kind, trying to hash out the finer points of his argument to his young, predominantly liberal fans. While Render apologized for the context of the interview, he did not retract any of his beliefs on the second amendment.
He's tone in his interviews has been noticeably more candid and open in recent times. "So my first challenge for Anthony Joshua is; be on time mate for the first time in your life".
A string of issues have kept him out of competition since then but we've seen a re-motivated Fury in recent months as he's dedicated himself to a strenuous training regime and ketogenic diet, which has seen him nearly return to fight shape.
Joshua believes Parker could be deterred in one of two ways. Straight away I knew this was a proper fighter who would go a long way.
I can't look past Joshua. Eddie should make an effort to get his man there on time.
"I don't think Anthony will be sleeping much this week and that could be why he's saying silly things". The 28-year-old will compete before a third big stadium crowd in a row after 90,000 saw him against Wladimir Klitschko nearly a year ago and 78,000 for October's fight against Carlos Takam.