Football's world governing body bans political, religious or commercial messages on shirts and had denied a Football Association (FA) and Football Association of Wales (FAW) request for a poppy to be displayed on their kits this weekend.
Chris Heaton-Harris MP, acting in conjunction with a senior Fifa adviser, called Fifa's secretary general Jerome Valcke on Wednesday afternoon and proposed his idea for the England team to wear black armbands with the poppy emblem.
“Fifa and The FA have to have a better relationship and I could see this situation was a recipe for disaster”
"Valcke instantly warmed to the idea despite the fact there was a protestor from the English Defence League (EDL) on Fifa's roof at the time," said Heaton-Harris.
"He [Valcke] understood the significance of the poppy but Fifa were in a position where, under the rules of the game, they couldn't sanction it being displayed on the England shirt.
"However, they were looking for a solution rather than an extra problem."
Heaton-Harris, with Fifa signalling that a potential deal was on, contacted the managing director of Club England, Adrian Bevington.
Once briefed, Bevington is understood to have then faxed a request to Fifa asking for permission for England to wear the amended armbands in their game against Spain at Wembley this Saturday.
Downing Street was kept informed of the proposed deal throughout Wednesday afternoon, with Prime Minister David Cameron alluding to the potential for a compromise in his letter to Fifa president Sepp Blatter which stated he hoped a "sensible solution" could be found.
Former FA chief executive Mark Palios: ''It's a move in the right direction''
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.