The presenter, who left the show in June to join ITV, admitted that the BBC One programme is still a huge part of her life.
She told the Daily Star Sunday: "I want myself and Adrian [Chiles] to go back to the show as guests - that would be brilliant. I'm very sentimental about the show because it was a massive part of my life.
"I'd love to see everyone again. All my friends still work on it. And I absolutely love Jason - I've been in contact with him ever since I left the BBC. He was always my first choice for a co-host when I was forced to think about working with someone other than Adrian."
Adrian Chiles also claimed that the pair can be very superstitious, saying: "Christine has to always sit on my left - it doesn't feel right otherwise. We went running together a lot while we were at the BBC and she had to be on my left even then. I also have to go into the studio after her - I can never go in first."
Bleakley added: "At first I played along because it made my life easier. But eventually I started to wonder what might happen if we didn't do these things. Now I'm superstitious too. We always rip the script at the same time after each interview and then throw it over our shoulders. It can get a bit daft sometimes.
"We can read each other's minds. We've got great chemistry and we have a love for each other as friends. When Adrian left the BBC I really missed that."
"Relationships like ours don't grow on trees," Chiles concluded.