According to the BBC the private Maha Bodhi Society said it was hoping to receive public donations to create the replicas of the giant statues carved from a cliff face in central Bamiyan.
All that is left is a hole where the statues once stood.
The organization said it would initially build a scaled down version of the larger statue, which was 51 metres (170 feet) tall, so that succeeding generations would know what it looked like.
Sri Lanka, where Buddhism is the major religion, had earlier offered to finance an international operation to save the statues, which were more than 1,500 years old.
The destruction of the giant statues provoked widespread international condemnation and criticism from Muslim leaders around the world.
Sri Lanka is hoping to buy remaining relics.
After the Taleban dynamited the monuments, claiming they were contrary to their Islamic beliefs, the Sri Lankan government offered to buy the rubble and any remains.
Prime Minister Ratnasiri Wickramanayake said he was also negotiating with other countries to buy other statues which remained undamaged in Afghanistan.
He said the cost was immaterial, as the statues were priceless and belonged to the whole of humanity.
Last week a group in India also offered to bring the rubbles of the two statues from Afghanistan and build replicas in India.
So far the Taliban have not responded to these proposals.
They have not yet allowed the international media to visit Bamiyan. Reporters have been waiting in Kabul for almost a week now and the Taliban have twice cancelled their scheduled trips.