Miley has posted a picture on Twitter of herself in bed kissing a cardboard cut-out of the One Direction star.
"All Noah Cyrus wants for her birthday is Harry Styles," she wrote, alongside a snap of her and her sister puckering up to Harry.
The former Hannah Montana star then posted a picture of herself alone with Harry under the covers, with her arm around the singer and closing her eyes.
Miley, who is engaged to Hunger Games actor Liam Hemsworth, later tweeted: "In no way do I want Harry. No offence. I'm sure that'll be a story now too. I'm happily engaged. Just got saucy with a cardboard cut out."
Harry and US country music singer Taylor are reported to have split following a bust-up in the Caribbean.
The British singer, 18, was pictured in a hot-tub with a blonde TV presenter and several others at Virgin tycoon Sir Richard Branson's private Necker Island after Taylor flew home alone from their break in Virgin Gorda.