The Saturdays singer has been romantically linked with the British royal after they were reportedly spotted together on a number of occasions.
However, she insisted that there is no romance, and that he is "out of her league".
She told Chris Moyles on his Radio 1 show: "I'm single, ready to mingle. No, I'm not going out with him - I'm serious. Everyone wants to believe it because it's royalty.
"Everyone would like it to be true but it's not. He's very out of my league, come on. I just went out with loads of friends and all of a sudden we're an item.
"But we're not. He must have so many girls after him, throwing themselves."
Her bandmate Frankie Sandford added: "When we heard the rumours we were all worried about ourselves, thinking that if she became royal we'd have to change around her."
"I think she's the catch. I don't think it would be all it's cracked up to be."
King recently stated that she is looking for an "old-school gentleman" to be her next boyfriend.