The source, speaking to AFP on condition of anonymity, said Garang's former rebel group, the Sudan People's Liberation Movement/Army (SPLM/A), had informed diplomats they thought their leader had perished in the crash.
"We have been told he is dead," the source said. "The SPLM believe he is dead."
Officials with the SPLM/A in Nairobi, where the movement was based for much of its 21-year war with the government in Khartoum, could not be immediately reached to comment.
Sudanese and Ugandan officials, who late Sunday said Garang's aircraft had gone missing on Saturday while flying from Uganda to southern Sudan, were not immediately available.
There have been conflicting accounts of the fate of Garang and the aircraft, which Sudanese officials say is a plane and Ugandan officials say is a Ugandan government helicopter, since it was first reported missing on Sunday.
Intitially, both SPLM/A and Khartoum said Garang was safe but the Ugandan military then said reports to that effect were incorrect, prompting a retraction by Sudanese authorities.
Late Sunday, Sudan's state television reported that Sudanese President Omar el-Beshir contacted his Ugandan counterpart Yoweri Museveni to try and locate the aircraft carrying the first vice president.
Garang had been in Uganda to meet with Museveni and a Ugandan military official said the helicopter carrying the ex-rebel leader and his entourage had left Museveni's ranch in the western Ugandan town of Rwakitura on Saturday during daylight.
At some point during the flight they encountered bad weather and tried to go around it. Radio contact was then lost and it is unclear what happened to the helicopter.
"There was bad weather, they tried to go around it but may have crash-landed somewhere," an official said.
Garang, who had been sworn in as Sudan's vice president only on July 9, played a key role in reaching the peace deal earlier this year, ending 21 years of civil war that killed more than two million people.