The pair were rumoured to be dating after the rugby player was spotted leaving a friend's house with Price shortly after her split from Leandro Penna last month.
The model is now hoping to incorporate an appearance on I'm a Celebrity... Get Me Out Of Here Now into her trip to secure a free flight to Australia, where Cipriani plays for the Melbourne Rebels.
"Katie's really into Danny. They got on well when they hooked up in London last month," a source told the Sunday Mirror.
"They initially said they should cool things off when he went back to Australia - but they can't stop thinking about each other. They have been talking loads on the phone and Skype and when Katie got the call from ITV2 it was the perfect opportunity to make things happen."
The source added that Cipriani's friends had warned him off Price.
Imogen Thomas branded Cipriani a "bulls**tter" after details of the fling emerged, claiming that Price was getting revenge for a past feud by spending the night with him.