Baradar was arrested in February during an apparent raid in Karachi by the Pakistani Inter-Services Intelligence Service and the CIA.
U.S. intelligence officials were reportedly seeking access to the Taliban leader, the highest-ranking figure captured since the Sept.11, 2001, attacks on the United States.
Islamabad initially denied the arrest was a joint operation.
Hamid Elmi, a spokesman for Afghan President Hamid Karzai, said Pakistan was discussing handing the Taliban leader over to Afghan authorities, Radio Free Europe/Radio Liberty report.
"Our interior minister and (the Pakistani) interior minister have had exclusive talks about this issue. They are ready to solve this issue and hand (Baradar) over to Afghanistan," he said. "They are working on solving the legal hurdles that could come in to place."
The spokesman said Kabul was looking for an agreement from Islamabad to obtain custody of all Taliban militant captured in Pakistan, however.
Islamabad at the time of Baradar's arrest was eager to dispel rumors allegedly spread by U.S. sources that Pakistani authorities orchestrated the arrest to undermine Afghan efforts to talk with the Taliban.
A Lahore court ruled in February that five captured Afghan Taliban leaders, including Baradar, wouldn't be extradited.