Last year, Musharraf purged the court, which was challenging his re-election bid. He also removed chief justice Iftikhar Mohammed Chaudhry.
The move deepened public discontent over his leadership, and Musharraf ended up resigning last month under intense pressure.
The issue of how to reinstate the judges, particularly Chaudhry, caused a rift in the ruling coalition of the Pakistan People's Party, led by slain prime minister Benazir Bhutto's husband Asif Ali Zardari, and the party led by former prime minister Nawaz Sharif.
Sharif has since withdrawn his party from the governing coalition.
Law Minister Farooq Naek said Friday that Chaudhry could take the oath, but could not return as chief justice because removing the judge who replaced him could trigger a "constitutional impasse," quoted the Associated Press.
Zardari also appears wary of Chaudhry, who stood up to Musharraf and questioned a pact signed by the former military ruler that quashed long-standing corruption charges against Zardari and his wife, the AP reported.
Zardari spent a total of 11 years in prison on charges of corruption and murder, although he denied all charges and was never convicted. He was released on bail in 2004, according to Reuters.
Zardari's decision to begin impeachment proceedings against Musharraf eventually led to the latter's resignation, clearing the way for Zardari to run for president. Analysts say a win by Zardari is virtually guaranteed.
In a letter published in the Washington Post, Zardari said the decision to run was not made lightly but because he wants to complete the country's process of becoming a democracy.
One of his first acts in office, he said, would be to change the constitution "to bring back into balance the powers of the presidency and thereby reduce its ability to bring down democratic governance."
His two rivals for president are Saeeduzzaman Siddiqui, a former judge nominated by Sharif's party, and Mushahid Hussain Sayed, a senior official of the party that backed Musharraf and ruled under him, according to Reuters.