The British designer is a huge fan of the eccentric 'Poker Face' singer's sense of style and would love to work with her - but only if she agreed with his ideas.
He said: "I'd love to dress Gaga but I'd be too terrified to tell her what to wear.
"It would have to be a collaborative process."
The designer's close friend, model Agyness Deyn, also confessed to being a big fan of Gaga and her quirky fashion ideas after seeing her promoting a new MAC lipstick.
Agyness told Now magazine: "I was inspired."
Henry and Gaga should get along fine if the designer creates an outfit with lots of accessories - including high-heeled shoes.
The singer said recently: "I would rather die than have my fans not see me in a pair of high heels. I'd never give up my wigs and hats for anything.
"You see legendary people taking out their trash, I think it's destroying showbusiness."