Staff from two shops in Lanark Road West and a member of the public contacted police on Saturday after receiving suspected fake notes.
The member of the public believes the notes came from a shop in Corslet Place, Currie.
All the notes that have been recovered are Clydesdale Bank 20 notes.
A police spokeswoman said: "It would seem that a batch of fake notes are in circulation in the area, so we would urge shopkeepers and customers to check any notes that are handed over in transactions.
"If anyone suspects they have been handed a fake bank note, they should hand it in to police for investigation.
"If you are unsure where it came from, take it to the local bank."