Katie had two children with Peter before their divorce in 2009, however relations are so strained that the pair only ever communicate through their respective other halves.
However, according to Kavana - who was evicted from the CBB house last night - Katie would like to offer an olive branch to her ex-husband and get back on speaking terms.
Kavana tells Reveal: "Katie did speak about Peter in the house. I think she'd be honest about it, because she says it like it is.
"I think she'd like a kind of reunion, so maybe they could speak again. I think she goes through text messages with the other half.
"She is on the side of having a chat with him, but according to her, it's Peter who doesn't want it."
Katie, who is now married to third husband Kieran Hayler, has spoken openly about her current and past relationships during her time in the CBB house.
The former glamour model has opened up about her sex life with both her second husband Alex Reid and her former fiancé, Leandro Penna, however viewers have not seen her chat about Peter.
A fortnight ago, we told how it was reported Katie had spoken about her divorce with Peter, but that the scenes were edited out in case they "jeopardised a forthcoming High Court battle" with the Australian singer.
When contacted about the claims, which appeared in the Daily Star, a CBB spokesman declined to comment.