But the PDP said on Thursday that the unusual circumstances in which Jonathan took over the presidency warranted a suspension of the zoning rules.
"We did not envisage that our dear president [Yar'Adua] would die in office," Okwesilieze Nwodo, the PDP chairman, told reporters ahead of a closed-door meeting of senior party officials with Jonathan in the capital Abuja.
"The party believes that Dr Goodluck Jonathan, as part and parcel of the joint ticket, has the right to contest the presidential primaries for the 2010 elections, but this would not preclude anyone in the party from contesting," Nwodo said.
Jonathan is said to be concerned that the suspension of presidential zoning would undermine his credibility in an election he has pledged to make free and fair.
But supporters warn that his failure to stand could trigger unrest in the volatile Niger Delta region, the heartland of Africa's biggest energy industry.
Jonathan has the support of powerful state governors in the south and central regions of the country, but northern Muslim governors have stopped short of endorsing him. Instead, they have simply acknowledged his right to stand.
Patrick Smith, editor of the London-based Africa Confidential magazine, said that Jonathan still has to secure his party's nomination in order to run.
"If the PDP allows a Jonathan candidacy, he will still have to fight for the ticket at the party congress, but there's little doubt that he will go for it and would be favourite to get the nomination," he said in an email.
"Jonathan's priority now has to be keep the party together - and that means making some concessions to his northern opponents."