The rock legend, who has performed on stage with the Hollywood star, has invited Johnny to come on tour with him and his band.
“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,” says the singer.
Johnny thrilled music fans at an intimate London gig last year when he joined Alice on stage as a surprise guest.
He rocked out to two of the rocker's hits School's Out and I'm Eighteen.
The Dark Shadows actor is keen guitarist and in the Nineties was part of his own band P – which included Flea from Red Hot Chili Peppers and Steve Jones from the Sex Pistols.
He definitely likes to keep his hand in – the 49-year-old took to the stage to perform with the Black Keys at the MTV Awards in June during one of the most memorable moments of the ceremony.
Half way through the show Aerosmith's Steven Tyler and Joe Perry took to the stage to present Johnny with the generation award, introducing a montage of clips from his career, including moments from Edward Scissorhands and Alice in Wonderland.
But instead of an acceptance speech, the handsome actor picked up his guitar and performed two tracks with rockers the Black Keys.
"It's like the get out of the business award, you've done too much," joked the screen idol of his award. "Based on the clips, there's obviously something wrong with me. I just thank you very much."
Johnny is currently single after breaking up with French actress Vanessa, his partner of 14 years and the mother of his two children.