Sara Anghel has not been seen since she left her home in the Inch yesterday afternoon, telling family she was heading to the Cameron Toll Shopping Centre.
The 15-year-old, who is originally from Romania, left Walter Scott Avenue at around 4pm but failed to return home.
Police have confirmed that they are in touch with port authorities to determine whether Sara and the man have made efforts to leave the UK.
Anyone with information is asked to come forward.
Sara is described as 5ft 4ins tall with a slim build, blonde shoulder-length hair and a dark complexion.
She was wearing a brown leather jacket with a fur collar, a black and white knee-length dress and a pink handbag.
Inspector Bob Innes said: “It is extremely unlike Sara to leave home without telling her loved ones where she is going, and even more out of character for her not to return. We are therefore very eager to trace her quickly and ensure she is safe.
“Anyone who may be in her company, or who has information as to Sara’s current location then please contact police immediately.
“I would also urge Sara to get in touch with her family, friends or with police to tell us where she is and that she is alright.”
Those with information can contact Police Scotland on 101 or alternatively, the charity Crimestoppers on 0800 555 111.