The speaker of the Swedish parliament Andreas Norlén has set a time table where the MPs will vote on either Social Democrat leader Stefan Löfven on the centre left or Ulf Kristersson of the Moderates on the centre right.
If a third and a fourth vote fail, a new election will be triggered.
And the two parties in the middle of the political spectrum, the Liberals and the Center party, are currently playing the roles of kingmakers in this.
But though the time is ticking, political scientist Sofie Blombäck at Mid Sweden University says it is still unsure whether the two parties will come down on the side of one or the other candidate this weekend.
Click on the link above, to listen to Sofie Blombäck's analysis of the political landscape ahead of the weekend.