On Friday, the leaders of the centre-left Social Democrats and centre-right Moderate Party will meet the parliamentary speaker to update him on any progress made over the Christmas break.
The three also spoke directly after Christmas, but a statement from parliamentary speaker Andreas Norlén merely said that he had “taken note of their respective assessments of the process of government formation”.
All the party leaders have been similarly tight-lipped, confirming that talks have taken place but with no hint of what the next government might look like.
Norlén has already named January 16th as the date when the next prime ministerial candidate will face a parliamentary vote. But it is not yet clear who this candidate will be.
Two such votes have already been held, with both incumbent prime minister Stefan Löfven of the Social Democrats and his centre-right counterpart, Moderate Party leader Ulf Kristersson, failing to gain enough support from parliament.
By far the most likely scenario is that one of these two would be proposed for the role a second time.
A prime ministerial candidate does not need a majority of parliament to vote in their favour in order to be accepted, but if a majority vote against, the proposal will fail. This system, called 'negative parliamentarism', allows minority governments to rule thanks to abstentions or 'passive support'.
If this third vote is unsuccessful, a fourth vote would happen on January 23rd, Norlén has said. If one of these votes is successful, the new prime minister will officially take on the role and name their cabinet within a matter of days.
But if neither vote is successful, Sweden will need to hold a second election, which must then happen no more than three months after the fourth and final vote. Swedish elections are always held on Sundays, so the latest date this could happen would be April 21st.
This means that Sweden is in wholly untested waters. Previously, parliament has always accepted the first proposed prime minister.
After the September election left the two main blocs separated by just one seat, one of the big obstacles to forming a government has been how to handle the third largest political group in Sweden, the far-right Sweden Democrats.
The Centre Party and Liberal Party are part of a centre-right group, the Alliance, along with Kristersson's Moderates and the Christian Democrats. But the former two parties have refused to be part of or even support a government which would also rely on support from the Sweden Democrats.
However, Löfven's attempts to win over these parties (the Centre has just enough seats to allow him to pass a parliamentary vote) have also failed, since the Centre Party in particular also made a promise in the election campaign not to support the Social Democrats.
Löfven has hinted that he would be willing to make more concessions, but he will have to be careful not to lose the backing of the Left Party, whose abstentions he will also need to win a parliamentary vote.