New evidence obtained by the BBC appears to back up claims by former FA chairman Lord Triesman of wrongdoing by Fifa vice-president Jack Warner.
Fifa's ethics committee could now be asked to open another investigation.
An e-mail from Warner to Triesman in February 2010 is expected to form a crucial part of an FA report.
In it, Warner urges the FA to contribute towards the cost of purchasing the rights to show World Cup matches on giant screens.
Lord Triesman, speaking to a parliamentary select committee earlier in May, claimed four members of the Fifa executive committee made what he described as "unethical requests" during the bidding race for the 2018 World Cup.
Among those claims were allegations that Warner asked the FA for money to build an education centre in Trinidad and for the FA to buy TV rights to the 2010 World Cup on behalf of Haiti.
DAVID BOND'S BLOG
“One Caribbean football official was offered but refused cash to finance football development projects in their country”
In the e-mail, he writes: "If you can assist them in any way by contributing in part or in whole to the purchase of these rights I am sure all of Haiti will be eternally grateful."
He mentions that a company had bought the rights for $1.6m (£980,000) but that he would be able to "get this figure reduced substantially".
JACK WARNER'S E-MAIL TO LORD TRIESMAN
My apologies for this belated response to your wonderful offer of assistance to Haiti for which I am really pleased. The people need all the help that we can give. I made a visit to Haiti last weekend to meet with the President of the Haiti FF to ascertain first hand the needs of our football family. A report has since been done which outlined their needs and proposals to meet these needs in the short, medium and long term. The report is included for your information. Based on this, I will leave it up to you to determine the best options of the FA as to how you all can assist.The FIFA, besides financial assistance, is providing them with large TV screens placed at two football stadia (at which stadia football can no longer be played in the immediate future) so that all Haitians can see the 2010 World Cup. However before the earthquake owner of the rights had charged them $1.6million USD for the rights, a fee which they had agreed to pay. I have since spoken to the owners and can get this figure reduced substantially. If you believe that you can assist them in any way by contributing in part or in whole to the purchase of these rights I am sure all of Haiti will be eternally grateful.
Thanks again for any assistance you can give and I do look forward to hearing from you soon.
Fifa, the ultimate owner of outdoor broadcast rights to the 2010 World Cup, has told the BBC that no public viewing licence was ever granted for Haiti.
It says it had no discussions anywhere in the world for an amount as big as $1.6m, but its response poses serious questions over the deal Warner was trying to arrange with the FA.
On Wednesday Fifa announced its ethics committee would charge Warner and fellow executive committee member Mohamed Bin Hammam with bribery.
And although it is not clear whether Fifa's ethics committee will add this latest allegation to the charge sheet faced by Warner, it places yet more doubts over the probity of world football's governing body.
Warner has not responded to the BBC's attempts to contact him regarding this story, though he did deny Triesman's previous allegations.
Meanwhile, Fifa president Sepp Blatter, writing for the Inside World Football website, stated: "I take absolutely no joy in seeing my friends and colleagues of many years dragged before the ethics committee.
"I take no joy to see men who stood by my side for some two decades, suffer through public humiliation without having been convicted of any wrongdoing.
"Nobody is guilty until a judge has found him guilty beyond reasonable doubt."
The FA has launched its own inquiry, calling in QC James Dingemans to compile a report for Fifa.
Watch the BBC Panorama documentary
Fifa: Football's shame?
on iPlayer (UK only)