Parliament has already rejected Social Democrat leader Stefan Lofven and centre-right leader Ulf Kristersson as prime minister and the parliamentary speaker did not say which name he would put forward on Jan. 16.
"It is high time Sweden had a government," Andreas Norlen told reporters.
The centre-left and centre-right blocs are equally balanced after September's national election and the anti-immigration Sweden Democrats hold the balance of power.
But both blocs have ruled out a deal with the Sweden Democrats and all attempts to end the impasse have failed.
Norlen has two more attempts to pick a candidate for prime minister whom parliament can accept.
He said that if the third vote did not deliver a new prime minister, a fourth vote would be held on Jan. 23.
If that also fails, the earliest date a new election can be held is April 21.
(Reporting by Stockholm Newsroom; editing by Niklas Pollard and Andrew Heavens)
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