The 42-year-old opposition leader Nikol Pashinyan, from the "Way Out" (ELK) Party, who has led the protests, is the only candidate in the inter-parliamentary vote on Tuesday as the country's ruling Republican Party (RPA) has failed to nominate a candidate in its bid to ease tensions.
However, local media outlets reported early on Tuesday that the sole candidate for the post has announced in a video message posted on his Facebook page that the Republican deputies have made a decision to thwart the scheduled vote.
The Armenian National Assembly is holding a special sitting on the item of the country's Prime Minister's election.
The Armenian Constitution dictates that parliament will convene next week for another vote.
The party did not put forward Karen Karapetyan, the acting prime minister and a Sargsyan ally, as a candidate.
Shortly after the vote, Mr Pashinyan left parliament and headed towards the square, where tens of thousands of his supporters were gathered. Later, dozens of them took the floor to speak about Pashinyan's candidacy.
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"There is information that (former presidents) Serzh Sarkisian and Robert Kocharyan - the famous tandem - are planning to take back power", Pashinyan said during a nail-biting session of parliament in the capital Yerevan.
Mr. Pashinyan was the only nominee, but anyone who garners support from one-third of the members can stand next week.
The crisis in ex-Soviet Armenia, which has a population of about three million and has Russian military bases on its territory, is being closely watched in Moscow.
Pashinyan has pledged to keep Armenia close to Moscow, saying the changes he wants to make would instead focus on rooting out graft.
The ruling Republican party of Armenia has in Parliament 58, block "prosperous Armenia" - 31, the Alliance is "EFC" - 9, ARF - 7 mandates.