The guitarist, who has toured with both musicians, disclosed the collaboration during her appearance on the SDR show.
While Strauss is yet to be invited to work on the track herself, she reveals that the pair "loved" working together on the new material.
After discussing the differences between Cooper and Lovato's fans, the hosts mistakenly question Strauss over the two artists' lack of inclusion on her new solo album, The Call Of The Void, and asks whether she'd ever consider writing a song with them both.
"Well Alice is [on The Call Of The Void], actually. And actually Alice and Demi have already written a song together. Demi posted some studio footage, I've talked to both of them about it, they both said that it went amazingly well and they loved working with each other.
"So they have not asked me to play on it yet...but after I finished the Demi tour, they went into the studio together and did a co-write".
As to what the track may sound like, she continues: "I haven't heard the song yet, but I hear the concept of the song sounds very on-brand for both of them. So I'm hoping I get that call."
Since releasing her first heavy rock record Holy Fvck last year, Lovato has been continuing to earn her rock credentials with other big-name collaborations, such as Guns N' Roses guitarist Slash, who appears on her new track Sorry Not Sorry, a reimagined rock version of her 2017 pop chart hit of the same name.
The song is set to feature on her forthcoming album Revamped, which is comprised of other restyled rock versions of her older pop tracks.
If having worked with Slash and Alice Cooper wasn't enough to solidify her standing within the rock world, the singer also recently expressed interest to collaborate with Slipknot frontman Corey Taylor.
During a recent conversation on the Metal Ambassador Podcast, she said: "Someone I've always wanted to work with is Corey Taylor and, you know, obviously working with bands like Knocked Loose would be sick, too.
"So I think it's something that's on my wish list but hopefully I'll have some collaborations for Revamped. We're still working that out, though."