"The kidnappers are Al-Qaeda members and are demanding a ransom of $12 million," one of the tribal sources said.
The account could not be independently verified. Al-Qaeda has not claimed responsibility for the kidnappings.
Security officials in Hadramawt province, where the three aid workers were kidnapped, said that they had succeeded in identifying the kidnappers and that they belonged to "an Islamist extremist group," without naming the organisation.
And security officials in Sanaa said they had no knowledge of ransom demands, but that they had information that the three French nationals are "in good health."
"We do not have this information," French foreign ministry spokesman Bernard Valero said when asked about the tribesmen's claims.
"We have been engaged from the beginning in attempting to free our compatriots, and, in their interest, we must exercise the utmost discretion to preserve the effectiveness of our action," he said.
The three -- two women and a man -- were kidnapped in the Hadramawt town of Seyun, 600 kilometres east of Sanaa on May 28th.
The trio are part of the French non-governmental organisation Triangle Generation Humanitaire, and were working with a group of 17 Yemenis in Seyun.
A Yemeni security official had said their car was found on the road some 20 kilometres from Shibam, a city known as the "Manhattan of the Desert" because of its spectacular high-rise mud-brick buildings.
Foreigners have frequently been kidnapped in Yemen by tribes who use the tactic to pressure the authorities into making concessions.
More than 200 foreigners have been kidnapped in Yemen over the past 15 years, with almost all of them later freed unharmed.