Aziz, 68, served as Pakistan's prime minister from 2004 to 2007.
Released by the International Consortium of Investigative Journalists (ICIJ) and 95 media partners, the Paradise Papers, a global investigation that reveals the offshore activities of some of the world's most powerful people and companies, includes information about at least 31,000 persons or parties.
The Express Tribune reported that Aziz is linked with Antarctic Trust, which was set up by him, and includes his wife, children and granddaughter as beneficiaries.
The trust was not declared at any point during his stint as the finance minister or the prime minister.
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Also, in a 2012 internal memo, the law firm's compliance officer noted that Aziz had been accused by the Opposition of false declaration of assets, corruption and misappropriation of funds. Three years later, in a database of high-risk clients, law firm Appleby noted that a Pakistani court had issued three arrest warrants against Aziz in relation to the killing of Akbar Bugti, a prominent Baloch leader.
According to the ICIJ, Aziz's lawyers have said that he was not legally required to declare the trust to Pakistani authorities.
The same applied to the former premier's wife and children, his lawyers said, adding Aziz paid all applicable US taxes.
The purpose of the account, they said, was "to ensure that if he were to die, his assets would pass efficiently to his family".
Sharif, 67, was the chief casualty of the Panama Papers as he was disqualified by the Supreme Court this July after graft and money laundering was revealed in the sensitive data leak case.
Besides Aziz, former National Insurance Corporation Limited (NICL) chairperson Ayaz Khan Niazi has been named in the Paradise Papers.
Niazi is alleged to have connections with a trust and three offshore companies in the British Virgin Islands (BVI), set up in 2010 when he was the NICL chairperson.
Niazi's brothers Hussain Khan Niazi and Muhammad Ali Khan Niazi were shown as beneficial owners, whereas Ayaz, his father Abdul Razaq Khan and mother Fauzia Razzaq acted as directors.
The ICIJ and 95 media partners explored 13.4 million leaked files from a combination of leaked files of offshore law firms and the company registries in some of the world's most secretive countries.