It had been suggested that United could ask their youngsters to defend the Cup while the senior side contested the World Club Championship in Brazil in January.
"No offer of that nature has been made to us," said Edwards. "We have consistently said that every option was reviewed and our decision has been made."
But Thompson was far from dismissive of such a possibility. "The FA would certainly give this idea every consideration," he said. "The rules state that a club must field its best available team. In this case, that would appear to be the players left behind who have not gone to Brazil."
The Treble winners have been accused of devaluing the famous old competition by pulling out, but Edwards added: "I think that it would devalue the competition even more for us to play the youth team. What would the long- term ramifications of that be in terms of other clubs in the future?
"It has always been clearly understood that this was a strictly one-off situation and our decision has been made."
The Old Trafford chief was also keen to shift blame for the controversial decision away from the club.
"We would have preferred to have played in the FA Cup but we changed our minds purely because of the Government pressure," he told the Sunday Telegraph.
"The proof of that is that, when we were first approached to play in Brazil last January, we said an emphatic `no'. It was only when it was put to us that if we didn't play we would be putting the 2006 World Cup bid at risk and it would cost vital votes in the bidding, that we had to reconsider.
"The Government and the FA put it on our conscience."
United enjoyed the majority of the support as they beat Australia 1-0 in the second game of a two-match series yesterday. The pitch at the spanking new Olympic Stadium was much better than the terrible surface the United players endured in Melbourne and one player who clearly benefited was Ryan Giggs.
The Welshman was given licence to thrill after he was deployed in a free role and he was outstanding. He created an early chance for Dwight Yorke before he laid on the only goal after 25 minutes to the delight of the United contingent in the 78,000 crowd.
Giggs slid the ball through to Yorke, who had made a diagonal run to the right, and last season's top scorer with 29 goals duly slotted home past Jason Petkovic.
The European champions are masters at selling merchandise, so despite the sea of red in the 78,000 crowd it was little surprise to see United emerge in something completely different. Their new white tops and navy blue shorts, made them look more like Tottenham.
"We're always looking to expand our brand," Edwards said. "We are a brand, we're a worldwide brand and if by spreading the gospel that helps us to market ourselves worldwide, great, that's one of the things we aim to do."