The Scottish frontman said his band view Glitter's glam rock hits with affection and argued that he was musically comparable to The Beatles.
"Listen to [Glitter's] songs again and see what you think," he told The Sun.
"'Do You Wanna Touch Me', 'Rock And Roll (Part 2)', 'I Didn't Know I Loved You (’Til I Saw You Rock ’N’ Roll)' are ecstatic and fantastic.
"Those records are better than The Beatles."
Gillespie added: "When I was a little kid, I heard those songs on the radio and I loved them. I still love them.
"What The Beatles were for people in the '60s is what glam rock was for us. We love Glitter, we love Bolan, we love Roxy, we love Suzi Quatro."
Primal Scream release ninth studio album Beautiful Future on July 21.