Sharif, 67, and some of his family members are facing charges relating to their ownership of properties in London.
He resigned as prime minister in July after the country's Supreme Court disqualified him over undeclared income.
Three cases were registered by the National Accountability Bureau (NAB) on September 8 against Sharif, his children and son-in-law in the Accountability Court Islamabad, following the July verdict by the Supreme Court.
Dawn reported that the NAB Lahore office yesterday initiated the process to place the names of Sharif, his sons Hussain and Hassan, daughter Maryam and son-in-law Mohammad Safdar on Exit Control List (ECL).
According to the NAB Islamabad spokesman the members of the family may face travel restriction if listed on the ECL.
An accountability court had earlier declared Hussain and Hassan proclaimed offenders for skipping court proceedings in connection with the case.
On Thursday, the NAB had requested the ministry of interior to put Finance Minister Ishaq Dar's name on the ECL after an accountability court issued non-bailable arrest warrants for him.
Dar, like Sharif's sons, has continuously been absent from court proceedings in a case against him for owning assets beyond known sources of income.
A senior official told the paper on condition of anonymity that the NAB Lahore had written to its Islamabad headquarters requesting that Hussain and Hassan's names be placed on the ECL.
The NAB spokesman in Islamabad confirmed the other three names — Sharif, Maryam and Safdar — that had been recommended by the anti-graft watchdog Lahore to be placed on the ECL.
The official in the NAB Lahore said according to the procedure, they would first place names of Hussain and Hassan, who live in the UK, on the ECL and if they still did not appear before the accountability court, then NAB would request cancellation of their passports.
Sharif's family has been shuttling between Islamabad and London in recent days due to his wife Kulsoom, who is battling throat cancer.
The three cases against the Sharifs are related to the Flagship Investment Ltd, the Avenfield (London) properties and Jeddah-based Al-Azizia Company and Hill Metal Establishment.
The political future of Sharif, who leads the country's most powerful political family and the ruling Pakistan Muslim League-Nawaz party, has been hanging in balance since his disqualification. If convicted, Sharif could be jailed.
Sharif's family alleges that the cases are politically motivated.