McCullum's lawyer, Garth Gallaway, is expected to file the defamation claim in the High Court at Hamilton early next week.
An initial deadline for a suitable apology and retraction was missed.
McCullum, who is in India with the Kolkata Knight Riders, said he had no option but to take legal action.
''Mr Parker's paper makes some very serious attacks on my integrity, my honesty and my ethics as a professional sportsman,'' he said in a press release issued by his lawyers.
''I have endeavoured to resolve these issues with Mr Parker but have been unable to do so. He has left me with no choice but to defend myself and my reputation this way.''
Mr Parker could not be reached for comment yesterday. A message on his answerphone said he was in the Middle East on business for 10 days.
McCullum, who is paying for the case himself, is not seeking monetary damages from Mr Parker.
''I simply want his acknowledgment that the claims he makes are completely false.''
Black Caps coach Mike Hesson also issued a statement yesterday.
''I have seen the press release from Black Caps captain Brendon McCullum released today.
''I have similar concerns to him regarding the comments made by John Parker about me. I have taken legal advice and the matter is currently being dealt with by my lawyers. I have nothing further to say regarding the matter,'' Hesson said.
The so-called Parker group came together with the intention of gaining more influence on the board of New Zealand Cricket and used the sacking of Ross Taylor, and the ensuing public outrage, as a plank in its campaign.
The release of a document containing a 77-bullet point plan titled ''The Taylor Affair'', according to McCullum's lawyers, made ''false and highly damaging claims about Brendon McCullum''.
Mr Gallaway could not be reached for comment yesterday, nor could Mr Parker's lawyer, John Wiltshire who, along with Mr Parker, is a director of The Sport Management and Training Group.
Any legal action issued by McCullum and Hesson is expected to target the original recipients of the allegations as well as anyone, including media, who published, forwarded or broadcast it.
- Additional reporting: APNZ
