The Chug - a cross between a Chihuahua and the Pug - was found running loose the M62 near Birstall on Sunday, February 17.
Traffic on the motorway at junction 27 near Birstall ground to a halt after notices of 'animals in the road' were put up.
After an unsuccessful appeal to find the owner, Highways England has issued an updated which said that the dog will be put up for adoption next week.
Highways England said in a tweet: "Update to the 2 little dogs found on the #M62 on Sunday evening.
"They are both currently being looked after by Cliffe Kennels & Rescue at Hoylandswaine and are doing great. If no owners come forward to collect them, they will be available for adoption on the 26th February."