Greek newspapers reported his wife told the police she suspected her husband’s involvement in the killing when she woke up to find he was not in their apartment and tracked his phone to where Ross was staying.
The statement given to police by Ahmadzai’s American wife has been described as crucial to the investiagtion.
Police said Ross – who is known to family and friends as Lisa – had been volunteering with a refugee support group based in Athens.
She arrived in Greece on 26 June and stayed in the Keratsini area of Piraeus until 10 July.
Ross is believed to have died a number of days before she was found.
Greek officials contacted Interpol and American authorities were able to identify her fingerprints.
Her family described her as “kind, principled and selfless”.
“Her integrity was absolute, and she dedicated her life to helping others in need,” a statement said.