Mullah Baradar -- a top Taliban military commander and the group's No. 2 after Taliban chief and founder Mullah Muhammad Omar -- was captured this month in Karachi in a joint U.S.-Pakistani intelligence operation.
The handover request was made by FBI Director Robert Mueller during meetings with officials of Pakistan's Inter-Services Intelligence and other intelligence agencies, Dawn reported, citing sources.
Pakistani authorities told Mueller an accused arrested in Pakistan can only be repatriated to the country of his origin if he did not commit any crime in Pakistan, the report said.
Pakistani Interior Minister Rehman Malik told reporters his government would "definitely" consider Mullah Baradar's extradition to Afghanistan if Kabul made a formal request, Pakistan's Daily Times reported.
Appearing with his Afghan counterpart Muhammad Hanif Atmar, Malik said a treaty for exchanging prisoners between Pakistan and Afghanistan is likely to be concluded soon.