Sharif, 67, resigned during his third stint as prime minister shortly after the Supreme Court ruled on July 28 that he should be disqualified and ordered a criminal probe into his family's wealth.
Jan Achakzai, a PML-N official, told Reuters Sharif had filed three separate appeals in the Supreme Court.
"It is our right to seek a review," he said. "People of Pakistan haven't accepted the decision."
Achakzai said the same five-judge panel that decided on the disqualification would likely hear the review petitions.
Sharif's disqualification stems from the Panama Papers leaks in 2016 which appeared to show that Sharif's daughter and two sons owned offshore holding companies registered in the British Virgin Islands and used them to buy properties in London.
In April, the Supreme Court ruled that there was insufficient evidence to remove Sharif from office - by a split 2-3 verdict - over the Panama revelations but it ordered further investigations into his family's wealth.
The judges in July alleged Sharif did not declare a small source of income that the veteran leader disputes receiving.
Achakzai said the appeals sought a review of the disqualification on the basis that two of the five judges, who had already given a dissenting note in April's verdict, were not supposed to sit on the panel that gave the final ruling.
Sharif has kept a grip on the ruling PML-N party, which has a solid majority in parliament, and elected one of his loyalists, Shahid Khaqan Abbasi, as his replacement within days of the court decision.
Critics say Sharif remains in control of the country through Abbasi and is trying to undermine the judiciary.
Sharif's aides say he shows no signs of leaving politics and he recently called the Supreme Court ruling against him "an insult to the mandate of 200 million voters".
Last week he started a so-called homecoming "caravan" procession across the Punjab region where he derives his voter base, from the capital Islamabad to the eastern city of Lahore, drawing large crowds along the way.
(Reporting by Asif Shahzad; Editing by Nick Macfie)
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