Miss Squire, 21, has not been seen since vanishing more than a week ago, and Sunday marks 10 days since officers started looking for her.
Mrs Squire and her husband, Russ, had previously made emotional pleas for information about their daughter’s disappearance.
On Sunday, officers could be seen entering a property on Raglan Street, Hull, where a 24-year-old man was arrested on Wednesday night on suspicion of abducting the missing student.
Police could be seen leaving the property with evidence bags, and they also used a camera to search the drains of the terraced house.
Humberside Police announced on Saturday evening that they had been granted another 24 hours to question the arrested man.
The extension allows detectives to quiz the man until 9pm on Sunday.
The search for Miss Squire has seen officers scour gardens and alleyways around her home on Wellesley Avenue, and officers have repeatedly looked around the nearby Oak Road playing fields.
Large digital posters displaying the face of the missing student have also been placed around Hull city centre, and university students have been assisting police with their searches.
Detectives have previously said that they are continuing to treat her disappearance as a missing persons investigation.
According to police, Miss Squire was seen taking a taxi from a nightclub on the evening of Thursday January 31.
Officers said that she was dropped off near her home at around 11.29pm, and was then seen near a bench on Beverley Road around 10 minutes later.
It is understood that police are examining CCTV footage, obtained by ITV News, which shows a man getting in and out of a car minutes after the last sighting of the student, who is originally from High Wycombe, Buckinghamshire.
In the video, the unidentified man is seen opening the front passenger door and moving around, before getting behind the wheel and driving away at around 12.09am on Friday February 1.
Detective Superintendent Matthew Hutchinson said on Saturday: “We are still treating Libby’s disappearance as a missing persons inquiry. I have said previously that we are keeping an open mind as to her whereabouts and that is still very much the case.
“Our number one priority is to find Libby Squire and we are still conducting extensive searches and appealing for any information from the public.”