The 61-year-old singer thinks the former One Direction star is "very cute" but also has the talent and personality to top the bill on the world-famous music festival's Pyramid Stage next year.
Harry had previously been rumoured to headline the Worthy Farm extravaganza this June, but Sir Paul McCartney, Billie Eilish and Kendrick Lamar were given the honour.
Speaking to Best UK, the 80s pop star said of the 'Golden' singer: "Well I do think he's very cute. I have to stay.
"He's like a breath of fresh air. I love his voice; I love his fashion style.
"So yes, I have a wee crush on Harry. He should play Glastonbury next year."
The 'Kids In America' hitmaker confessed in a previous issue of the magazine that she fancies the 28-year-old singer - who is dating another Wilde, actress-and-filmmaker Olivia Wilde, 38.
Asked who her celebrity crush is, Kim said: "Don't laugh ... Harry Styles!
"If he walked into my house, I think I would blush."
Kim also recalled falling "passionately in love" with the late David Bowie when she supported him on tour, though she knew she wouldn't "get a look in".
She said: "I fell passionately in love with Bowie - but he was in love with his wife-to-be at the time, Iman - I didn't get a look in.
"I loved him from afar.
"As soon as I saw him, I thought, 'My God, you are the most incredible person.'
"How could you not love David Bowie?!"
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