The Echo and the Bunnymen frontman performed last night at a JD Set concert in Glasgow celebrating Bowie, alongside Sharleen Spiteri, Steve Mason, Kate Nash and Ramona.
McCulloch told DS: "I'd love to do one last great David Bowie song. I'd love me and him to do something. I've got songs that I'd love him to sing - it was him and Leonard Cohen.
"I just think Bowie was so influential and the greatest solo artist of the 20th Century. In any walk of art. It seems like he's waiting [to release new music]. Maybe his life's just changed."
Bowie's last studio album was 2003's Reality. The singer-songwriter was diagnosed with an acutely blocked artery while on tour the following year and underwent an emergency angioplasty.
Of his own band's decision to tour 1984 album Ocean Rain again, McCulloch said: "It was always in the back of our minds - well in the back of my mind anyway.
"The first gigs we did at the Royal Albert Hall, Liverpool [Echo] Arena and New York were probably the favourite shows that I've ever done."
He added of the album: "It's got everything on it - it's so unusual - and the sound of it is quite unique. The way it was done it sounds completely different from everything else we did.
"From the start to finish, ending with 'Ocean Rain'... In the liner notes on our box set, Wayne Coyne from The Flaming Lips said that was the defining moment of rock and roll for him - hearing the waves."