Speaker Andreas Norlen could give the nod to outgoing prime minister Ulf Kristersson, who heads a caretaker government after narrowly losing the election.
On Monday, the leader of the Social Democrats, Magdalena Andersson, threw in the towel after failing to form a government following more than a week of talks with three other parties in her left-wing bloc due to deep ideological differences.
The speaker could still ask Andersson to try again.
The left won 176 seats in the election, three more than Kristersson's right-wing bloc which includes the far-right Sweden Democrats.
Kristersson would be hard pressed to secure a parliamentary majority.
He said following the election that he was ready to explore options to find a majority among "non-socialist" parties.
He is seen as wanting to court the Centre Party, which is now part of the left-wing bloc but used to belong to the right-wing.
Centre Party leader Elisabeth Thand Ringqvist has however refused to support any government that gives any influence to far left or far right parties.
Kristersson, in power since 2022 thanks to the unprecedented support of the far-right, had vowed the anti-immigration party would be given cabinet posts for the first time if the right-wing won the election, though he has in recent days backtracked on the idea.
The parliament speaker has four chances to put a candidate prime minister to a vote in parliament before a new election has to be called.
Sweden has become accustomed to lengthy negotiations to form a government. After the 2022 election, it took 37 days, and 134 days in 2018.
Most observers have predicted that Kristersson would likely fail if tasked with forming a government, and the speaker would then solicit Andersson again, who would ultimately manage to unite her bloc under pressure to avoid a new election.
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