The leaked track, called 'So Legit', features lyrics such as: "You're looking like a man, you're talking like a baby/ how the f*ck is your song in a coke commercial, crazy?"
The song is thought to be from when Del Rey recorded under her real name Lizzy Grant and shared a manager with Lady Gaga.
"Stefani, you suck, I know you're selling 20 million/ Wish they could have seen you when we booed you off in Williamsburg/Have we all gone Gaga crazy?," asks a further line, referencing Gaga's real name Stefani Germanotta.
It's likely the song was written around the time of Gaga's breakout success in 2008/2009, while Del Rey was still and up and coming artist.
However, Del Rey's representatives are yet to confirm whether it is legitimate and the leaked song has now been removed from YouTube.
The 27-year-old released her debut album 'Born To Die' in 2012 to critical acclaim and recently sang on 'The Great Gatsby' film soundtrack.