AQAP militants are demanding the release of female Al-Qaeda-linked prisoners held in Saudi Arabia in return for Khalidi’s release.
They have also held a South African couple since May.
Hundreds of people have been abducted in Yemen in the past 15 years, nearly all of them later freed unharmed.
Kidnappings are often carried out by tribesmen who use their captors as bargaining chips in disputes with the central government.
A Dutch couple abducted in Yemen last month issued an impassioned plea in an Internet video this month for their government to act to secure their release, warning they face execution.
Journalist Judith Spiegel and her partner Boudewijn Berendsen appear in the minute-and-a-half clip posted on YouTube and Facebook and dated July 13.
“We have been kidnapped here in Yemen and we have a big problem,” said an emotional Spiegel sitting next to Berendsen.
“These people are armed. If a solution is not found within 10 days, they are going to shoot us.”
In early May, members of a southern tribe freed three Red Cross employees, including a Swiss and a Kenyan, along with two Egyptian hostages, following tribal mediation.
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