Moss, who hooked up with the musician only a month ago, sent the message to her close friends after a 12 hour romp with Hince.
"I love Jamie so much - we're engaged," the Mirror quoted Moss, as saying.
However, her friends say that the engagement is not formal, and that Moss is just expressing her love for Hince.
A friend said that the 34-year-old is sending out a clear message to ex flame Pete Doherty that she is really happy.
"Kate and Jamie had been together all night and day until 5pm and when they surfaced Kate told her friends that she and Jamie were engaged", a pal said.
"No one thinks they are actually going to walk down the aisle any time soon - they know it was Kate's way of saying she's serious about him."
"Everyone knows it's a message to Pete too, telling him she's moved on and is happy with her new man."