Svetlana Gannushinka, a human rights worker, told Britain's Guardian newspaper it was "not clear whether he's [Khachukayev] a hostage or a defendant"
"As soon as I found out about his kidnapping I faxed the office of the interior ministry at Vnukovo airport. They didn't answer," she said.
A string of Kadyrov's critics and political rivals have been murdered in recent years in Russia, Austria and Dubai.
Earlier this year, two human rights advocates were abducted in Chechnya and killed.
The bodies of Zarema Sadulayeva and Alik Dzhabrailov were found in Grozny, in August, a day after being abducted from their offices by masked men.
Their murders came a month after the death of Natalya Estemirova, one of the best known activists in Chechnya and head of the Memorial group, who was abducted in Chechnya and found in neighbouring Ingushetia.
Ongoing attacks against human rights activists has led Memorial and other human rights organisations to suspend their operations in Chechnya.
Last month, a Moscow court ordered Oleg Orlov, head of Memorial, to retract his accusation that Kadyrov was responsible for Estemirova's death.