Judge Petrus Damaseb, the deputy-chairman of FIFA's ethics commission, has asked FIFA secretary general Jerome Valcke to consider a new probe into some of those that attended the meeting in Trinidad on May 10 and 11 where the cash gifts were said to have been paid.
The three FIFA members who accompanied Bin Hammam on his private jet were Manilal Fernando from Sri Lanka, Worawi Makudi from Thailand and Hany Abo Rida from Egypt.
All three have told investigators they did not see cash gifts being offered, nor was there any talk of that taking place.
Of the 24 associations from the Caribbean Football Union at the meeting, where Bin Hammam was speaking about his campaign to be FIFA president, nine told investigators they were given or offered cash gifts of 40,000 US dollars each. The other 15 denied receiving any cash gifts or refused to meet investigators.
FIFA have yet to comment on any new investigation but Damaseb said at a press conference at the weekend: "In the light of the evidence disclosed in the investigation and the hearings, the ethics committee decided to ask the secretary general to request a further investigation into the conduct of others who attended the meeting of 10 and 11 May in Trinidad and whose conduct justifies further investigation."
The investigation into the bribery claims was carried out by the Freeh Group International (FGI) Europe - the private investigative agency owned by ex-FBI chief Louis Freeh.
The Freeh report to the ethics committee, a copy of which has been seen by the Press Association, states: "Mr Fernando, Mr Makudi and Mr Abo Rida said they did not observe cash or any gifts transported on the private jet that brought them to Trinidad and Tobago.
"Each also said that there were no discussions by Mr Bin Hammam about bringing cash or gifts to the CFU meeting. Mr Fernando, Mr Makudi and Mr Abo Rida also said that they did not observe any cash or gifts exchange hands in Trinidad and Tobago."
Part of evidence collected by Freeh stated that FIFA vice-president Jack Warner, who had the investigation against him dropped after he resigned from football activities, told the CFU delegates after Bin Hammam's address to attend a room to collect their gifts.
Fernando told investigators he could not recall that happening. Makudi said the same but, according to the report, added "that he stepped out of the room after Mr Bin Hammam's remarks to the attendees, because he needed to make some telephone calls".
Abo Rida also said he did not recall hearing Mr Warner telling attendees to pick up a gift that afternoon but that he "had some difficulty understanding Mr Warner's remarks".
Four associations did not respond to invitations to meet investigators - Anguilla, Antigua and Barbuda, Dominica and Montserrat.
A further 11 associations did send officials to meet investigators but denied receiving cash gifts. They were Barbados, Guyana, British Virgin Islands, Dominican Republic, Haiti, Jamaica, St Kitts and Nevis, St Lucia, St Vincent and Grenadines, Trinidad & Tobago, and United States Virgin Islands.
The Freeh report also includes statements about Colin Klass, a CFU executive committee member and president of the Guyana FA, who orchestrated a campaign by other associations to write letters backing Warner and saying there was no offer or talk about cash gifts at the Trinidad meeting.
The report quotes evidence from Bahamas vice-president Fred Lunn, who took a photo of the cash he was given before returning it on the afternoon of May 10, stating that Klass went into the room when the money was being given.
The report states: "Outside the boardroom, Mr Lunn encountered Lionel Haven (a former Bahamas FA board member) and Colin Klass.
"According to Mr Lunn, Mr Klass stated: 'why is this door locked, are there people getting bribed around here?' The male [CFU official] then allowed Mr Klass to enter the boardroom, which he exited after a few minutes. Mr Lunn noticed that Mr Klass had a smile on his face and was slightly giggling."
Klass told investigators however that he did not go into the boardroom.
The report states: "Mr Klass tried to enter the CFU boardroom on the afternoon of May 10, but was told that the room was not for him. Mr Klass remembered that Mr Warner said on May 11 that the only gifts were a laptop computer and projector.
"Mr Klass... stated that [he] had not been offered or received any cash gift while in Trinidad and Tobago at the meeting."
Bin Hammam warned that the trio of FIFA members who accompanied him to Trinidad who would be "victims" of FIFA's revenge against him for standing against Sepp Blatter for president.
Bin Hammam told Sky News last night: "I am telling you there were three members of the executive committee of FIFA travelled with me to Trinidad and Tobago and supported me actually during the campaign.
"These will be the coming victims also because it is their revenge. We are in the court of the kangaroo. We are subject to revenge for that we dared. First of all I dare to be a candidate, sometimes I find some people in Europe are very strange. They talk a lot about democracy but they are the last people in the world who like democracy. And if you see our world of sport that anybody hold the chair will kill anyone who tries to come close to it."