Properties across the city and beyond have been targeted in different incidents between November 20, 2023 and February 3, 2024.
The thieves have hit homes in Robroyston, Maryhill, Bearsden, Bishopbriggs, Hogganfield, Garthamlock, Kelvindale, Jordanhill, Govanhill, Nitshill, Newton Mearns and Darnley.
They usually strike in the late afternoon or early evening.
While detectives do not have evidence which confirms they are linked, they have noted similarities between each case.
They believe four cars could be linked to the incidents – a black BMW Series 1, a white Volkswagen Golf, a black VW Golf, and a grey Audi RS3.
The force is urging anyone to come forward if they think they might have any information regarding the crimes.
Detective Inspector Ross Jamieson said: “I am appealing to anyone who may have seen any suspicious activity involving the vehicles mentioned.
“I appreciate many of these crimes took place some time ago, but I would ask people to think back and consider if they saw anything odd or suspicious.
“We are keeping an open mind about whether these incidents are linked and there are significant similarities between each of the crimes which indicates they could be connected.”
If anyone has any information, please contact Police Scotland via 101 or call Crimestoppers on 0800 555 111 where you can give your information anonymously.