Humberside Police distributed the video 18 days after the student was last seen during a night out in Hull.
The clip shows a cyclist, a pedestrian and a pair walking together in the early hours of 1 February, the last day the 21-year-old was seen.
Officers said they all appear to have come from the direction of areas including the playing fields where investigators have conducted searches.
Detective Superintendent Martin Smalley said: "These four people are potentially witnesses who we need to identify and speak to as part of the investigation. While the footage isn't clear enough for anyone to recognise who they may be, the four people in the clips will know if they were in that area at the times given and I would ask them to please come forward to assist with our inquiries."
The footage is the latest attempt by police to work out what happened that night to Miss Squire. Searches to locate her are ongoing.
Anyone who recognises individuals in the footage is asked to contact police on 101.
Additional reporting by Press Association
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