Sri Lanka, the seat of Theravada Buddhism, had earlier offered to finance an international operation to save the two statues, which date back more than 1, 500 years.
Presidential aide, Lakshman Jayakody, said that he believed Sri Lanka had the expertise to reconstruct the statues.
"We have the expertise and experience in erecting such statues," Jayakody said.
"We want to make a formal request to get what is remaining of the Bamiyan Buddha statues."
Sri Lanka's Prime Minister Ratnasiri Wickremanayake and Foreign Minister Lakshman Kadirgamar made separate visits to Pakistan in a bid to pressure the Taliban to spare the priceless statues.
On Friday, the Taliban Supreme Leader Mullah Mohammad Omar ordered 100 cows to be sacrificed to atone for delays in the destruction of the ancient statues in the central Bamiyan province.
"These cows are to be slaughtered by the Islamic Emirate of Afghanistan (Taliban) for the further glory of God, the Almighty's name and as an offering for the error and the delay in the destruction of the statues," Radio Shariat reported in Kabul.
Under Omar's "special instruction," 100 cows will be slaughtered on Monday and the meat distributed to the poor.
Omar, a student of the Koran, war veteran and recluse, two weeks ago ordered all statues in Afghanistan to be destroyed to stop idolatry, regardless of their historical importance.
The dynamiting late last week of the two colossal statues in Bamiyan provoked widespread international condemnation and strong criticism from Muslim leaders.
The Taliban, an international pariah only recognized by Pakistan, Saudi Arabia and the United Arab Emirates, argue their iconoclasm is an "internal religious issue."
