GaGa is said to be a huge fan of the late French singer and has enquired about purchasing collections of her clothes, shoes, perfume bottles, private letters and even toenail clippings.
"GaGa sees a lot of herself in Edith," revealed a source. "She, too, was a rebellious character in her era."
GaGa - who reportedly plays Edith's music as her entrance theme at parties - is said to be keen to mark the 50th anniversary of the 'Non, Je Ne Regrette Rien' singer's death by incorporating songs and footage into her own performances.
The paper claims that GaGa's representatives have been in talks with the Piaf estate about buying the rights to her first filmed performance and have spoken to label EMI about using nine of her songs as samples on the 26-year-old's next album.
It is thought that the 1941 film footage would then be broadcast on stage alongside the tracks during GaGa's next tour.
"There's an awful lot of red tape to get through," the source said. "It's a complicated process. But she's hoping the Piaf estate want to ensure, with her help, that the music can be introduced to a new audience.
"Considering the size of GaGa's global following, Edith's music will gain a huge new fanbase."
GaGa, who is currently touring Europe in support of her album Born This Way, was recently awarded The LennonOno Grant for Peace in recognition of her charity work and activism.
Watch Edith Piaf perform 'Non, Je Ne Regrette Rien' below: