Her husband, Steven, and brother, David Jimenez, travelled to Istanbul to help in the search and were interviewed by Istanbul police Tuesday. The two left police headquarters after about seven hours and were seen carrying a suitcase, which the state-run Anadolu Agency said belonged to Sierra.
Sierra's belongings, including her passport, were found in her hostel room.
Jimenez did not immediately respond to questions sent by email or to an interview request.
Police have released security camera footage showing Sierra alone, eating in the food court of a shopping mall and walking along a main shopping street near her hostel. She is dressed in jeans, a brown leather jacket and a winter hat.
Sierra had planned to go on the trip with a friend but ended up going by herself when the friend couldn't make it. She was looking forward to exploring her hobby of photography, on her first trip outside of the U.S., her family said.
Associated Press writer Ezgi Akin contributed to this report.