The couple, who have been dating since October, recently enjoyed a post-Valentine's Day romantic break to Dubai.
Writing in her OK magazine column, Katona said that she had used the leap year to offer a marriage proposal to the warehouse worker.
"I would marry Steve in a heartbeat if he ever asked me and I actually asked him twice to marry me on February 29," she said. "But he didn't respond and instead just made a joke of it, even though I was being sincere.
"I'm also very old-fashioned - I think it's wrong for a woman to ask, but he's missed his chance now anyway!"
Upon returning from the trip, Katona thanked Alce on Twitter, writing: "You've changed my world I love you (sic)."
Describing him as "the one", the Celebrity Big Brother star said that living with Alce was "going really well".
> Kerry Katona: 'I've found love again'