The 24-year-old penned Mi Amorosa Aventura, which translates as My Love Affair, after spending his first season with Sir Alex Ferguson's side which has so far seen him find the net 18 times.
The Argentina striker fronts a band in Buenos Aires called Piola Vago (Sly Idol), and a source told The Sun: "He has fallen deeply in love with Manchester United, the players, everything. He is full of emotion for the way he has been taken into their hearts.
"He can't believe it when he hears United fans chant 'Argentina' - especially with the history between the two countries.
"He wants to put it all into words. He is in a band with his brother Diego and they are very popular back home. He will record the song when he returns in the summer."