The 56-year-old singer wrote the track 'Two Steps Behind Me' about the 'Pokerface' hitmaker in which she describes her as a ''copycat'' and compares her to a ''messed-up sister'', reports The Sun newspaper.
Madonna sings: ''You're a copycat, Where is my royalty? You're a pretty girl, I'll give you that. But stealing my recipe, it's an ugly look.
''Did you study me hard enough? You're never gonna be, you're just a wannabe me. Like a sister all messed-up, who's gonna help you out? In your fantasy, you can try it all. But you can't be me.
''You can walk the walk, even talk the talk. But you'll always be two steps behind me.''
A source working closely with the 'Holiday' singer on her upcoming 13th album thinks Gaga, 28 - who counts Madonna amongst her idols - will be ''mortified'' when she catches wind of the damning lyrics, although it is yet to be confirmed whether the song has made the cut.
They said: ''They're very harsh lyrics but Madonna really wants to express herself again. Gaga's going to be mortified.
''I'm hearing Madonna may well drop the first of the tracks as soon as November, much earlier than expected. I can't wait.''
Madonna also attacks her ex-husband Guy Ritchie in the lyrics to another track 'Heartbreak City' in which she describes the memory of their relationship as ''haunting'' and accuses him of using her for fame.
She sings: ''Cut me down the middle, f***ed me up a little. You said I was your queen. I tried to give you everything. And now you want your freedom.
''You got just what you came for, a bit of fame and fortune, and I'm no longer needed.
''You tore me into pieces, you didn't have no damn reason. I let you in my kingdom, you helped yourself with everything.
''I curse the day we met. This memory is haunting me. I wish I could forget.''
Madonna was married to the director from 2000 to 2008. The former couple have a son Rocco, 14, and an adopted son, David, eight, together.
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