Infantino's proposal was short-lived after a fierce backlash from across the sport, with European governing body UEFA threatening to boycott all FIFA competitions until it was shelved.
FA chair Debbie Hewitt, who is also a FIFA vice-president and a member of the FIFA Council, has written to Infantino asking for full disclosure of all information relating to the scheme before the FIFA Council next meets on October 15th.
Hewitt has also called for the release of documents relating to the decision to suspend a ban handed to United States striker Folarin Balogun during the World Cup, which followed a phone call from US President Donald Trump to Infantino.
Infantino apologised over the process in regard to the private investor plan in August and a statement from FIFA's management board pledged there would be a review but has not at any stage confirmed who is undertaking that investigation.
UEFA said it has "lost confidence" in Infantino and has made legal applications in the US court system seeking disclosure of documents related to the private investor plan.
UEFA has also committed to identifying a credible candidate to run against Infantino at the FIFA Congress in March, with November 18th the deadline for candidates to be submitted.
Infantino confirmed earlier this month his intention to seek re-election.