The 70-year-old singer - who has had more than 130 singles in his career, which has spanned more than half a century - would love to work with the eccentric singer but only if she toned down her notorious costumes.
He told BANG Showbiz: "I wouldn't mind singing with Lady Gaga but she can't wear any of those hats."
In addition to Lady Gaga, Cliff - who has been a bachelor his whole life - is also respectful of Leona Lewis and Adele, proclaiming them both to have "fantastic" voices, but he is concerned about how long their respective careers will last.
He added: "Adele and Leona Lewis are both incredible, fantastic voices but only time will tell. My gripe is that often with these really fine singers something goes wrong through no fault of their own and then they disappear. I hope Adele can hold her own because she sounds fantastic!"
Discussing his own taste, Cliff claims he likes an "eclectic" mix of artists.
Cliff's forthcoming new album - an as-yet untitled collection of duets with both soul legends and contemporary artists - has been produced by Lamont Dozier, with David Gest serving as executive producer.