The UN representative says he proposed to the Taleban that an international group of Islamic scholars look into the matter, or that threatened objects be shipped out of Afghanistan.
UN special envoy to Afghanistan Francesc Vendrell, who has just returned from Kabul, says he spoke at length with Taleban officials but received no assurances that the edict would not be carried out.
Official and opposition sources, quoted by the French news agency AFP, said Taleban fighters had launched an attack on the Buddhas with rockets, tank shells and even automatic rifles.
The report is unconfirmed - journalists have not been allow to visit the area - but it follows a Taleban announcement earlier in the week that all graven images in the country would be destroyed.
"If it is true the international reaction is going to be extremely negative," he said. "I think it would be a shocking thing to do."
The world-famous statues at Bamiyan are unique, the taller of the pair standing at 53 metres (125 feet) high.
They date back to between the second and fifth centuries AD, before the coming of Islam, when Afghanistan was a centre of Buddhist learning and pilgrimage.
Earlier it was reported that explosives had been brought to the Bamiyan site to blow up the statues, but the latest reports say impatient fighters have taken the matter into their own hands.
"People are firing at them out of their own sentiments," a militia source was quoted as saying.
On Thursday, the movement said it had started to destroy all the statues in the national museum in the capital, Kabul, as well as in museums in Ghazni, Herat and Farm Hadda, near Jalalabad.
International alarm
The Taleban - a hard-line Muslim movement - has dismissed international pressure to save the statues, declaring them "idols" which are "insulting to Islam".
The UN representative says he proposed to the Taleban that an international group of Islamic scholars look into the matter, or that threatened objects be shipped out of Afghanistan.
India has called the destruction of the artefacts a "regression into mediaeval barbarism" and has offered to arrange the transfer of all artefacts for the benefit of mankind, while stressing they remain the treasures of the Afghan people.
Buddhist countries such as Nepal, Sri Lanka and Thailand have also denounced the Taleban's move.
The Metropolitan Museum of Art in New York has offered to buy statues rather than see them destroyed.
A Taleban spokesman in the United States, Sayed Rahmatullah Hashmi, told the BBC the statues were being destroyed to retaliate for the 1992 demolition of the ancient mosque at Ayodhya in India by Hindu activists.
Meanwhile, the movement's representative in Pakistan, Salem Zaeef, denied reports that the destruction of Buddhist statues had begun at all.