Miss Pope, 19, who is from Langton Matravers, Dorset, has not been seen or heard from for nearly a week.
The man and woman, who police say were both known to Miss Pope, were arrested after officers raided two homes in Swanage.
She has been released on bail under investigation. The male suspect remains in custody.
Miss Pope was staying at an address in Swanage when she disappeared on 7 November.
CCTV captured her running along the pavement on Morrison Road at around 4pm. She was running in the direction of a house in Manor Gardens, where she was last seen alive.
At the time she was said to be wearing a red checked shirt with white buttons, grey and white woven leggings and white trainers.
Describing her disappearance as completely out of character, police now believe she may have come to harm.
Detective Chief Inspector Neil Devoto said We have looked through CCTV that covers the Swanage area, including transport hubs, and there is nothing to suggest she has left the area.
We have not yet found Gaia and our searches will continue.
Dorset Police have also carried out house-to-house inquiries in the Swanage area, and are appealing to anyone with information to get in contact.
Last week Miss Pope’s family urged her to get in touch We are all frantic with worry Gaia and are desperate to know you are okay.
You are not in any trouble and we just want to know you are somewhere safe.
Please get in touch with someone to let us know where you are so we can help you.
Miss Pope is described as 5ft 7ins tall, with long mousy blond hair.
News Source SkyNews