The 40-year-old actor reached out to Murphy, 28, Monday evening on Twitter following the singer's elimination in Sunday's episode of American Idol.
Many viewers, including Gad, thought Murphy was "robbed" after he was eliminated during the Showstopper Rounds of American Idol Season 19.
In his tweet, Gad asked Murphy to write a song for his show Central Park, an animated series that will return for a second season on Apple TV+ in June.
"Hey @Blindboy_music you were robbed on @AmericanIdol and I would love for you to honor us by writing a song for us on #CentralParkTV - DM me," he wrote.
Murphy responded, saying, "I'd be honored. :) Dming you now."
Murphy was a fan favorite contestant during his time on American Idol. He performed the original song "Am I Still Mine?" during Sunday's episode after sharing how he has a degenerative eye condition that will likely leave him blind by the time he's in his 30s.
Gad is known for voicing the snowman Olaf in the Frozen movies.