Oli stepped down last week ahead of a no-confidence vote in the parliament, which he was expected to lose.
Unified Maoist chief Pushpa Kamal Dahal is the lone candidate running for prime minister.
The Nepali Congress, the biggest party in parliament, and a number of smaller parties have said they would support Dahal.
Dahal needs a two-third majority in the 601-member house to be elected.
Dahal, also known as Prachanda, or the fierce one, led the Maoist guerilla movement during the civil war from 1996 to 2006, in which more than 16,000 people died.
The Unified Maoist party joined mainstream politics in 2008. Dahal also served as prime minister from August 2008 to May 2009, but he was forced to step down after he attempted to sack then-army chief, Rookmangud Katawal.