The legendary rock star made a surprise appearance in the Rock of Ages musical in the West End last night to celebrate the 40th anniversary of his track 'School's Out'.
The pair appeared together in Tim Burton's recent Dark Shadows, and the Pirates of the Caribbean star joined Cooper on stage at London's 100 Club last year.
Depp also recently played guitar live on stage with the Black Keys at the MTV Movie Awards, and has collaborated with Marilyn Manson on his most recent album.
The 64-year-old has now said that he'd love to have Depp accompany him on a more regular basis, telling The Sun: "Johnny came to Hollywood to play guitar. He didn't come as an actor at all.
"I always say to him, 'If you really want to go out on tour, let me know and you can come with us'. I wouldn't be surprised if he did."
Cooper appeared at the Bloodstock Open Air festival in Derbyshire this weekend (August 9-11), and will be embarking on a seven-date UK tour in November.
Watch Alice Cooper perform 'School's Out' on The Muppet Show below: