Zardari told Pakistani media that he would announce whether or not he had accepted the nomination within 24 hours.
The coalition government is struggling to tackle economic problems in the country, unrest in the tribal areas and the growing strength of Taliban loyalists.
Meanwhile, Nawaz Sharif, leader of the Pakistan Muslim League, the second largest party in the ruling coalition, had suggested that the next president should be from one of the two smallest provinces, Baluchistan or North West Frontier.
That would exclude Zardari, who hails from the southern province of Sindh.
Judges decision delayed
Nominating Zaradari became mired in wrangling over other issues, principally how to restore judges purged from the supreme court when Musharraf imposed emergency rule last year.
But Sharif, two-time prime minister whom polls suggest is Pakistan's most popular politician, has repeatedly threatened to go into opposition if the judges are not restored quickly.
On Friday, he set next Wednesday as a deadline for the judges to return to the bench, the third such ultimatum since Musharraf stepped down.
"Wednesday should be the day for reinstatement of judges," Sharif said.
At the same time, Pakistan's election commission announced that a presidential election would be held on September 6 to choose Musharraf's successor.
Although the PPP and Pakistan Muslim League-N party were able to agree on impeaching Musharraf, the issue of the judges has threatened to divide the coalition.
Sharif said that representatives of the PML-N party and the PPP would draft a resolution on restoring the judges over the weekend .
Parliament is then expected to vote on the issue on Wednesday.
"We do not want to quit the coalition and wish to go along with our coalition partners," Sharif said.
Musharraf deposed the 60 judges, including the chief justice, after placing Pakistan under emergency rule in November.
Babar Sattar, an Islambad-based political analyst, told Al Jazeera: "It seems like the PP have no intention of actually restoring the judges, they are just bidding for time.
"Parliaments don't really make policies, parties make policies, and there is no political party in the parliament right now. Even the opposition has moved a resolution to restore all judges, including Iftikar Chaudhry," he said.
Raja Assad Hameed, a special correspondent for the Pakistani newspaper The Nation, told Al Jazeera: "There is rallying support behind Pakistan People's Party chairman Asif Ali Zardari, to be the presidential candidate."
"Nawaz Sharif has been distanting himself from nominating Zardari and he has been saying that ... somebody [less] political and controversial [should be nominated by the ruling coalition instead] so that he could emerge as the symbol of the federation and president of Pakistan."
Nomination papers for the presidency can be filed from August 26 and the final date for any withdrawals will be August 30, Kanwar Dilshad, the election commission secretary, said on Friday.
Under Pakistan's constitution a president is elected by members of the country's four provincial assemblies and the national parliament within 30 days of the post becoming vacant.