The ITV breakfast presenting duo would both receive £2m if they were let go, just a year into their three-year deals, The Mirror claims.
However, a source told the paper that bosses have ruled out dumping Chiles and Bleakley, adding: "We got stiffed on the deal. We can't pay them millions for nothing."
An insider continued: "It's a common thing in television.The original faces on GMTV didn't work, it was only when it was overhauled after six months on air that they became successful.
"The same needs to be done here. People have had a look at Christine and Adrian in the mornings and said, 'No thanks'. There was too much hype and fanfare about them. The show is horribly underperforming and needs to be fixed.
"We spent £15 million on Daybreak and we've gone backwards. It needs sorting. But Christine and Adrian are an expensive headache."
When presenting financial results for 2010 earlier this year, the broadcaster stated that Daybreak had "not performed as we would have hoped".
Responding to the latest claims, an ITV spokesman said: "We have no plans to change Daybreak's presenting team. Daybreak has continued to see steady growth in viewing particularly amongst housewives with children and younger viewers, and we continue to listen to feedback from our audience and develop the show."
ITV hit back at similar claims in April, at the time insisting that the show is "fully committed" to both Chiles and Bleakley.
> Bleakley: 'Daybreak has turned a corner'