France qualified for the 2010 World Cup at Ireland's expense after Henry blatantly handled the ball as he set up William Gallas for the decisive goal in a play-off match in Paris in November 2009.
Delaney's claim comes amid a corruption scandal engulfing FIFA that has seen president Sepp Blatter announce his resignation and former executive committee member Chuck Blazer admit to paying bribes.
Delaney said that Blatter's behaviour at the Soccerex football conference in Johannesburg 11 days after the match had hardened his resolve over the matter of compensation.
"The way Blatter behaved, if you remember on stage, having a snigger and having a laugh at us..." he said.
"That day when I went in (to discuss the agreement), and I told him how I felt about him, there were some expletives used."
Henry was derided as a cheat in the aftermath of the match at the Stade de France, which ended in a 1-1 draw that saw France win 2-1 on aggregate.
The FAI and the Irish government unsuccessfully petitioned world governing body FIFA for the game to be replayed or for Ireland to be admitted to the World Cup in South Africa as a '33rd team'.
Henry, then with Barcelona, backed Ireland's calls for a replay and declared himself "extremely sorry", but rejected the accusation that he was a cheat.
France went on to endure a disastrous World Cup, crashing out in the group phase after the players went on strike in protest at striker Nicolas Anelka's exclusion from the squad for clashing with coach Raymond Domenech.
-AAP