At 6.10 pm emergency services received reports that a black BMW X5 was on fire on the hard shoulder of the northbound M74, three miles north of junction 17.
A witness reported seeing “one or perhaps two people” getting out of the car and leaving the scene on foot.
Police are looking to trace the individuals who were in the car and said they “may have left the motorway across nearby fields and may have been carrying a bag or suitcase”.
Inspector Colin McKinstry said: “I am appealing to anyone who has not spoken to us and may have information or dash-cam footage that could help with our enquiries to get in touch.
“I am also appealing to those inside the car to get in touch, by calling Police Scotland on 101 quoting incident 2637 of Tuesday, 5 October, to let us know that they are safe and well.”
Anyone who can help is asked to contact Police Scotland on 101, quoting incident 2637 of Tuesday, 5 October.”
