The council commissioned high court judge Jeff Blackett, the RFU's disciplinary chief, to undertake a review of the process which led to Steele's departure after just nine months.
One of the recommendations contained in the 52-page report is believed to have said that then-chairman Martyn Thomas and the majority of the board should resign.
The report was considered at the last board meeting on July 10, at which Thomas did stand down - although he insisted that was only to concentrate on his role as acting chief executive.
The council voted against publishing the report after Thomas' lawyers threatened to sue Blackett for defamation during the meeting.
A vote of no confidence in the board was also defeated at the meeting by a majority verdict.
As a result, the report was kept confidential - but since then at least 24 council members are understood to have signed a motion, which has been submitted to the RFU, demanding publication.
The Daily Telegraph has reported that all council member received a letter outlining the possible ramifications of publishing Blackett's findings.
The newspaper claims that legal opinion was given by Deputy High Court judge Robert Englehart, QC, who concluded that publication would be "inadvisable".
The RFU has been engulfed in turmoil since Steele was ousted from his post on June 9 after losing the confidence of Thomas and the board.
Central to Steele's downfall was the RFU's botched attempts at recruiting a performance director.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.