The couple discovered the young royal python in the bathroom of their flat on Storie Street on 17 November.
They contacted the Scottish SPCA, which rescued the snake and named her Lulu.
A spokesperson for the charity said it was believed that the snake had got in through a gap in the wall by the toilet pipe and then wrapped itself around the seat.
It is being cared for at the charity's Glasgow Animal Rescue and Rehoming Centre in Cardonald.
Ch Insp Fiona Henderson said: "The lady who found her got quite a fright, but did the right thing by containing the snake in the room and calling us for help.
"Pythons are generally known for their placid nature and relatively small size, so although they can look a bit scary, they aren't dangerous.
"We're keen to reunite Lulu with her owner, who probably lives close by.
"She's in good body condition and well fed, so we're sure someone is missing her."
Anyone who recognises Lulu is asked to contact the Scottish SPCA.