The timing of the announcement is unknown, except that it will come at some stage after the three-day period during which the royal court has accepted condolences for the death of Sultan, and not necessarily on Thursday.
But Prince Nayef, long the interior minister of the world's top oil exporting state, is likely to be named the new crown prince, succeeding Prince Sultan who died of cancer last week.
At stake is the stability of a U.S. ally which wields great influence over Sunni Muslims through its guardianship of Islam's holiest sites in Mecca and Medina.
Conservative even by Saudi Arabia's austere standards, Nayef is sometimes portrayed as putting the brakes on the king's cautious political reforms. Earlier this year he publicly admonished a member of the mainly consultative Shura Council who had called for a review of the ban on women driving.
However, some diplomats and analysts say Nayef, who was born in 1933 and has served as interior minister since 1975, may show a more pragmatic side as crown prince -- and eventually as king.
An Allegiance Council of the ruling family, set up by the king in 2006, is expected to approve his nomination of a new crown prince.
King Abdullah, who was born in the early 1920s, has had no designated successor since Sultan's death on Saturday but the council can step in if anything befalls the ruler before an heir is named.
U.S. Vice President Joe Biden was due to arrive in Riyadh on Thursday to offer condolences to Washington's main ally in the Gulf.
Senior members of the ruling family, including Nayef and Riyadh Governor Prince Salman, received high-ranking foreign officials and royals who came to pay respects in Riyadh.
They included Britain's Prince Charles and Defense Secretary Philip Hammond, reflecting Sultan's position as both crown prince and defense minister of a kingdom with close ties to the British arms industry.
Nayef has already run Saudi Arabia on a daily basis for extended periods in recent years, during absences of both King Abdullah and Crown Prince Sultan.
Given the king's age and health problems, the new crown prince is likely to assume an even more active role immediately.
"There is an institutionalized mechanism in place," said Hossein Shobokshi, a Saudi columnist. "The Crown Prince had been deteriorating for some time so they haven't been caught by surprise. It should be extremely orderly.
"We had been waiting for this development and things will be announced from a protocol point of view after the mourning period is over."
The kingdom opposed the Arab Spring popular uprisings that have caused instability in neighboring Yemen and Bahrain, fearing they might help to increase the influence of its major Gulf and regional rival, Shi'ite Muslim Iran.
Nayef was quoted soon after the Sept. 11, 2001 attacks on the United States as doubting that any Saudis had been involved. It turned out that 15 of the 19 airline hijackers were Saudis.
About 60 percent of Saudis are under the age of 30 and, with Internet penetration of 44 percent according to internetworldstats.com, are increasingly outward-looking.
King Abdullah's cautious reforms, opposed by conservative clerics, have aimed to create more private sector jobs, reduce the role of religion in education and improve the prospects of Saudi women.
The king may also make a wider cabinet reshuffle. The position of second-deputy prime minister, held by Nayef since 2009, is usually awarded to the prince who is considered third in line to the throne.
Although King Abdullah does not have to name anyone to the role, and did not appoint Nayef as second-deputy until four years after he became king, it might be seen as an important fail-safe given Abdullah and Nayef's ages.
Prince Salman, a younger full brother of Sultan and Nayef, is widely seen as the most senior prince after Nayef and the most likely to be given the role.
Prince Salman is thought to have been born in around 1936 and is the father of the country's tourism minister, Prince Sultan bin Salman, who in 1985 became the first Arab astronaut.
Former diplomats to Riyadh say he has a reputation as religious, and has wide experience dealing with foreign governments due to the country's many expatriate workers.