The court on Sunday summoned the birth registration, passport, educational certificate, and other documents regarding Zia's date of birth from her.
Officials said the Law Ministry reviewed the legal scope and barriers for Zia's visit abroad and sent its opinion to the minister.
Dhaka Tribune reported that one of Zia's relatives, who had met her last week, had later tested positive for the coronavirus.
Zia and Hasina are known as the 'Battling Begums' for their bitter rivalry that has poisoned Bangladeshi politics for nearly three decades.
Bangladesh court sentences ex-Prime Minister Khaleda Zia to five years in prison on corruption charges
Zia, leader of the opposition Bangladesh Nationalist Party was found guilty of stealing $252,000 from a trust created for an orphanage.
Former PM and BNP chief Khalida Zia and five others stand accused of embezzling 21 million takas in foreign donations meant for the Zia Orphanage Trust.
Bangladesh police banned street protests Tuesday ahead of a verdict against opposition leader Khaleda Zia, whose party says more than a thousand of its activists have been detained.