Al-Qaeda militants abducted the woman on March 14th from her home in the Red Sea port city of Hodeida, where she had been teaching at a foreign language institute.
She was taken to far eastern Shabwa province.
Tribal chief Ali Abdullah Zibari said, however, that mediation efforts had so far failed because of excessive demands placed by her captors, including the release of bin Laden's widows held in Pakistan.
Zibari said the Islamic extremists also demanded the release of several women held in Iraq and Saudi Arabia in return for the Swiss captive.
"Their initial demands for the release of (former Al-Qaeda chief) Osama bin Laden's wives held in Pakistan were rejected by Yemeni officials last week," Zibari told AFP, adding the group then placed new conditions for the Swiss woman's return.
"Now they're demanding the release of 100 Al-Qaeda affiliated militants from Yemeni jails and €50 million ($66 million)... at which point the mediation efforts failed because of the prohibitive demands," he said.
Zibari played a crucial role in the release last November of three French aid workers kidnapped by Al-Qaeda and held for five months.
Shabwa province is a stronghold of Al-Qaeda's local affiliate, the Partisans of Sharia (Islamic law), which has expanded its influence in recent months, taking advantage of the political turmoil that has swept the country and forced the resignation of veteran leader Ali Abdullah Saleh.
Kidnappings were common even before the uprising against Saleh's rule that began last year.
More than 200 people have been abducted in Yemen over the past 15 years, many of them by members of the country's powerful tribes who use them as bargaining chips with the authorities.
Almost all of those kidnapped were later freed unharmed.