Most observers believe it will increase its present tally from five to ten seats in the Irish parliament, which has 166 seats in all.

Sinn Fein has already declared its readiness to talk to the Republic's larger parties about the possibility of coalition after the election. There is, however, strong opposition to any such move across the political spectrum.

This means Sinn Fein would only be included in a coalition, or even included in some informal deal, if some major party was desperate and could find no other suitable partners.

At the moment, the polls indicate that when voting takes place next Thursday the result will be inconclusive. A hung parliament would trigger a round of inter-party negotiations as the major players seek to put together a majority.

Depending on the arithmetic, Sinn Fein could find itself either at the centre of negotiations or left frustrated on the sidelines.

The dream would be to gain entry to a Dublin government. Earlier this month Sinn Fein became part of the power-sharing administration in Belfast, with its chief negotiator, Martin McGuinness, taking the office of Deputy First Minister.

Most Irish politicians say, however, that Sinn Fein's association with the IRA is too recent for it to be treated as anything like a conventional political party. The political system in general dreads a situation where Sinn Fein could hold the balance of power in the next parliament.

Most of the other parties would not even entertain an arrangement with Sinn Fein, but there is a widespread belief that, despite public declarations to the contrary, the Fianna Fail party might think of it if there was no other choice.

Bertie Ahern, the outgoing prime minister, and other party figures have ruled out a coalition or other type of pact with Sinn Fein. The public tends, however, to take a sceptical view of such statements, which have in the past been subject to hasty post-election reappraisals.

In an opinion poll earlier this year, when voters were asked whether they believed Mr Ahern when he said he would not be dependent on Sinn Fein votes, 31 per cent said they believed him but 46 per cent said they did not.

In the election campaign, Sinn Fein has made several adjustments to policies which might have scared off voters, ditching plans for increased taxation of the well-off and a hike in corporation tax.

The party's left-wing approach has nonetheless been denounced during the campaign by the right-wing Progressive Democrats as "a decline in the student politics of the 1960s - Marxist dream stuff".

Asked about the declarations that other parties would not go into power with Sinn Fein, Gerry Adams, the party president retorted: "Ian Paisley was saying the same thing." Insisting his party was "ready for government" in Dublin, he added: "We are not interested in being in government for the sake of it. We don't want to see Sinn Fein bums on ministerial seats just for the craic."

The possibility of a post-election deal was raised by one leading bookmaker, Ivan Yates, who was once a member of the Irish parliament. He said: "Nobody has mentioned the elephant in the sitting-room, but whatever way you cut it Sinn Fein are going to hold the balance of power.

"I think people who have been slow to shake Gerry Adams's hand before the election will be giving him a bearhug after the election."