The couple, who have found fame on the fly-on-the-wall reality series, are contracted to the channel and hope this will boost their chances!
Speaking to Sarah Powell on Heat Radio, Stephen even encouraged fans to back their suggestion by launching a campaign.
When Sarah suggested them for the role, Stephen revealed: "Everyone keeps saying that to us! I think that there should be a campaign - Chris and Stephen for Bake Off!"
Chris then pointed out: "We are signed to Channel 4 don't forget. And also, I like to make cakes and [Stephen] likes to eat them. If we were offered, yeah we would do it - because I love a soggy bottom."
Stranger things have happened!
Following the shock news that Love Productions had agreed a big bucks deal to move GBBO from the BBC to Channel 4, current hosts Mel Giedroyc and Sue Perkins quit. Baking queen Mary Berry has also confirmed she will not be moving, out of loyalty to the BBC, but Paul Hollywood has agreed to make the switch.
The new lineup is yet to be revealed, however several faces have already been forced to DENY they are joining the show. On Monday night, Jennifer Saunders and Dawn French described rumours they would present the new series as "b*llocks". Meanwhile, Alan Carr, Davina McCall and Jamie Oliver have also quashed claims they will be taking the helm.
Sarah Powell is on Heat Radio every Monday to Friday, 4-7pm