Any hope the Republic of Ireland had of being allowed into next year's World Cup finals as a 33rd team has been ended by Fifa.

Sepp Blatter, president of football’s governing body, revealed on Monday that the Republic had asked to be added to the tournament after failing to get their play-off with France replayed.

They are angry that Thierry Henry’s handball in the build-up to William Gallas’s decisive goal – France won the two-legged tie 2-1 on aggregate to book their place in South Africa – was not spotted by any of the match officials.

Jerome Valcke, Fifa’s general secretary, bluntly ruled out entering an extra team into next year’s tournament at a press conference on Tuesday. The draw for the tournament, which runs from June 11 until July 11, will take place in Cape Town on Friday.

“There’s no hope to give that there will be any more than 32 teams at the World Cup,” said Valcke.

“We had 853 qualifying matches, it is sad that we are talking about just one game. I wouldn’t say [Ireland’s complaint] is a nonsense but it is impossible.”

The Fifa executive committee are expected to formally reject the Republic’s request at their meeting on Wednesday.