Blatter revealed the Irish request at a conference in Johannesburg
Fifa officials are to meet with the Football Association of Ireland to discuss the controversial handball goal in the play-off against France.
Financial compensation for the Irish has been ruled out but Fifa president Sepp Blatter revealed other measures were being considered.
He explained the ideas ranged from a compliment to a special award.
The Republic lost 2-1 on aggregate to France whose winning goal came after Thierry Henry's blatant handball.
Earlier, Blatter had apologised to the FAI for revealing that it asked for a 33rd place at the World Cup.
"I regret what I created by what I said and I'm sorry about the headlines," said Blatter on Wednesday.
"The Irish were very sporting people when they came to see us at Fifa. I'm very sorry about that."
Blatter said the FAI had written to withdraw their request, made when they felt they had been cheated out of a World Cup place by a handball by Thierry Henry that led to an aggregate winning goal for France in their European zone play-off match.
Blatter had been branded a 'loose cannon' and 'an embarrassment to Fifa' by Ireland's assistant manager Liam Brady for revealing details of a supposedly private meeting with Irish officials last week.
The former Arsenal and Juventus midfielder said the Irish federation believed its meeting was private and confidential.
"Mr Blatter is a law unto himself and I thought it was very disrespectful," Brady said.
Brady added that the Republic knew all along that there was very little chance of their request being granted but had decided to make it anyway on principle.
"We asked because we wanted them to respond in a measured way and see what they would say," he explained.
The Irish request was discussed at an extraordinary meeting of Fifa's executive committee on Wednesday but football's governing body had already said there was no chance of accommodating them in the 2010 World Cup field.
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