The singer came under scrutiny last year with the release of her single 'Born this Way', which some critics claimed sounded far too similar to Madonna's 1989 hit 'Express Yourself'.
Gaga dismissed the accusations, saying that claims that the song was based on Madonna's track were "retarded".
However, Madonna said of the song: "I thought, 'What a wonderful way to redo my song'. I mean, I recognised the chord changes. I thought it was... interesting." She later described Gaga's music as "reductive" in an interview on Nightline.
In the footage - which is believed to be from rehearsals at the Ramat Gan Stadium, Tel Aviv - the 53-year-old star sings lyrics from 'Born this Way' over the music for 'Express Yourself'. The medley ends with a rendition of 'She's Not Me' from Madonna's 2008 album Hard Candy.
Some now believe that the 'Like a Virgin' singer may be trying to make a dig at GaGa, who recently was forced to cancel a Indonesian concert on her own tour due to threats from religious groups.
The 'MDNA' tour launches in Israel on Thursday (May 31). Madonna has yet to comment on the audio.
Watch Madonna's medley during the 'MDNA' tour rehearsals below: