The 12-member family had originally been scheduled to leave for Saudi Arabia overnight for illegal entering and residing in Pakistan, but their lawyer said that they had not received their passports yet.
The former al-Qaeda leader's family was detained in Pakistan after bin Laden was killed by the US Special Forces last May in the garrison town of Abbott bad, north of Islamabad.
The widows and two of bin Laden's older daughters began serving a 45-day prison sentence on charges of illegally residing in the country on March 3 when the court case was filed.
On Tuesday, the family completed their 45-day sentence.
They are likely to be deported to Saudi Arabia on April 18, as their sentence ends on April 17, Aamir said.
They were scheduled to leave Pakistan for Saudi Arabia late Tuesday but the problem in completing their travel documents delayed the departure, Aamir said.
According to Aamir, bin Laden's youngest and reportedly favourite wife, Amal Abdulfattah, who is Yemeni, might be sent to Yemen with her five children.
Al Arabiya television earlier this week showed footages of bin Laden's widows and children under house arrest in Islamabad.