With the largest number of seats, it falls to the PPP to name a prime minister. On Saturday, Farhatullah Babar, the party's spokesman, said a decision was imminent.
"Our party will come up with a name next week," he said.
Parliament would then have to confirm the nomination.
Mohammedmian Soomro, the caretaker prime minister, has held the office since November, after parliament's mandate expired and before new elections could be held. Soomro presided over the last cabinet meeting on Saturday in Islamabad.
Among those considered frontrunners for the position is Makhdoom Amin Fahim, the PPP vice-chairman and a veteran politician whose father helped Bhutto's father, Zulfikar Ali Bhutto, establish the party in the 1960s.
On Saturday, Fahim called himself a "strong candidate" and said he was puzzled by the PPP's delay in naming him.
"What have I done wrong to my party?" he told Pakistan's Express news channel.
Addressing rumours that he had fallen out with the party's leadership over an alleged secret meeting between him and Pervez Musharraf, the Pakistani president, Fahim said: "If anyone saw me meeting with Musharraf, he should come forward and say it."
The PPP's delay in naming Fahim or another candidate has fuelled speculation that Asif Ali Zardari, Bhutto's widower, who jointly leads the party with the couple's 19-year-old son, wants the job for himself.
On Friday, an anti-corruption court quashed the last outstanding graft charge in Pakistan against Zardari, in a case involving the import of a German limousine.
A money laundering case is still pending against him in Switzerland.
The ruling lifted a potential roadblock to Zardari taking a role in the cabinet. Pakistani law bars anyone convicted of a crime from holding office.
Since his wife's death, Zardari has become an increasingly key decision-maker in Bhutto's party as well as in Pakistan's opposition movement.
But many Pakistanis view Zardari as a symbol of the corruption and misrule by civilian governments that nearly bankrupted the country in the 1990s. They know him as "Mr 10 Percent" for allegedly pocketing kickbacks when his wife was prime minister.
Zardari spent years in jail without being convicted and insists all the graft charges were politically motivated.