The 78-year-old victim was targeted by two men who offered to carry out maintenance work at her home in Carntyne in the city's East End last Thursday, between 1.30pm and 3pm.
She handed over a four-figure sum of cash after the men had started work but they left before the task was complete.
Police have launched an appeal for information regarding the two suspects, described as white, Scottish, and wearing high-visibility jackets.
One is 5ft 9, of stocky build and in his mid 40s. The other is about 6ft, of medium build, mid to late 20s and has short brown hair.