The Swiss parliament is to vote on a successor to Ruth Dreifuss on Wednesday.
The race to replace Dreifuss, a Social Democrat, looks likely to be between her party's two official candidates, but an unknown contender could still launch a challenge.
"I'm not 100 per cent convinced that parliament will not surprise us," political analyst Julian Hottinger told swissinfo.
"It could pull a candidate out of the bag that we have never heard of or have not been expecting."
Under the Swiss system, parliament chooses cabinet ministers in a secret ballot, and parliamentarians are free to nominate any candidate they please - irrespective of whether they are on the official ticket.
Cabinet seats are allocated according to a convention dating back to 1959 - commonly known as "the Magic Formula."
It ensures that there is a representative balance in government among the four main parties with the Social Democrats, the Christian Democrats and the Radicals each taking two posts and the rightwing Swiss People's Party, one.
The Magic Formula also takes into account linguistic and regional representation. The replacement for Dreifuss is widely expected to be a French-speaking Social Democrat - just like the retiring interior minister herself.
Even though the Social Democrats have officially nominated two candidates, Micheline Calmy-Rey and Ruth Lüthi, a surprise could still be on the cards.
Political analyst Hans Hirter says the outcome is hard to predict as anyone can stand in the first two rounds.
"Someone else may throw their hat into the ring," he told swissinfo. "And those voting may decide to switch their allegiances."
When the People's Party put forward two official candidates in the December 2000 election to replace their outgoing minister, Adolf Ogi, neither of them was elected. Instead parliament chose another member of the People's Party, Samuel Schmid.
As none of the parties in government has more than 25 per cent of parliamentary seats, they rely on each other's support to secure the election of their candidates.
The People's Party has also put forward a candidate, Toni Bortoluzzi, although he is widely thought to stand no chance of being elected.
"The People's Party is making a point," said Hottinger. "It is not trying to get its candidate in[to the cabinet] - instead it is reminding everyone that it is one of the four major parties in government, and is against the Magic Formula."
The People's Party's real purpose, according to Hirter, is to make it clear to the electorate that it will be launching a serious challenge for a second seat in the cabinet after next year's general election.
"The People's Party wants everyone to see that it thinks it is the only true party representing the Right," he said.
Even though the free cabinet seat is to all intents and purposes "reserved" for the Social Democrats, Hottinger believes it is still important to go through the voting procedure.
"If the Social Democrats were simply allowed to appoint someone to replace Dreifuss, it would take away the little power parliament has," he said.
"The truth is that parliament does not really take any major decisions - they are made through referenda and initiatives."
He says the process also legitimises the party's candidates and will give the winner credibility in representing the Social Democrats in government.
"It is a coalition government in which all parties have agreed to share power," he said. "It is a coalition in which every [political] force in the country is more or less represented."
A joint session of the House of Representatives and the Senate will meet at 8.00am on Wednesday.
Theoretically all Swiss citizens are entitled to be candidates for the first two ballots, but no new candidates may stand after the second round.
With every further ballot, the person with the least number of votes is eliminated from the race.
The winner must receive an absolute majority (half of the votes, plus one).
The Social Democratic Party has nominated two candidates to contest the vacant cabinet seat.
Cabinet seats are divided among the four main political parties in a power-sharing arrangement known as the Magic Formula.
The outgoing Social Democrat minister, Ruth Dreifuss, should be replaced by a politician from the same party.
The vote is a free one conducted by a secret ballot of all members of parliament.
The new cabinet minister will have to secure at least 124 of the 246 available votes.