The couple have moved in together and Jordan has pledged to quit drinking and get fit to please him.
The model's step-grandad, Tom Price, 62, told Closer magazine, "She's never really wanted to get married before but Peter seems a great bloke and I think it's the real thing this time, particularly now they've moved in together.
"It is really serious. Katie is closer to Peter than she's been to any other boyfriend."
The celebrity couple's romance has blossomed since they first me in I'm a Celebrity...Get Me out of Here.
But, according to a close friend, Jordan has confided, "I'd marry Peter tomorrow."
Tom, 62, from Saltdean, near Brighton, added, "Peter seems like a really nice guy and gets on fabulously with Harvey. He dotes on him. It's early days but they are very lovey dovey together. All the right ingredients are there and I think and hope they will marry."
One of the model's first boyfriends, Gary Bolingbroke, 32, told Closer, "I think Katie should marry Peter. He seems a lovely geezer and they would make a great couple."
Jordan, 25 says, "I want to have more children, a proper family with the man I love - and that's Peter. I never say I'm in love usually. I don't know what he's done to me, but I'm besotted with him."
