Abdullah Abdullah had issued what he called minimum conditions for the runoff following the disputed first-round vote and set Saturday as the deadline for authorities to implement them.
Al Jazeera's Jonah Hull, reporting from Kabul, the Afghan capital, quoted Abdullah's campaign as saying that it would hold a news conference to discuss the matter on Sunday.
"His spokesman [says] that a final decision hasn't yet been made by Dr Abdullah to react to the fact that many of those conditions have not been met," our correspondent said.
"We're now told [Abdullah] is in intensive meetings; he is still making up his mind."
The first round of voting on August 20 was so badly affected by ballot-box stuffing and distorted tallies that more than one million votes were thrown out.
The fraud pushed Hamid Karzai, the president, below the required 50 per cent margin needed to win, forcing the country into a second round to be held on November 7.
Abdullah has accused the country's electoral commission of being complicit in the fraud.
Abdullah's conditions for the runoff to take place included the dismissal of Azizullah Ludin, the government-appointed co-ordinator, to ensure a fair vote.
But both the Karzai campaign and the election commission have said that Ludin will not step down.