It was reported last month that talks between the broadcaster and the reality show's production company Endemol were at "an advanced stage". Davina McCall has suggested that she will not host the series if it does make a comeback.
Speaking to Digital Spy, Byram - who presented US reality programme Paradise Hotel - confessed that she would not be keen on replacing McCall.
"I always kind of question that kind of thing, bringing it back," she said. "It's like making a sequel. I don't know - it's like drinking from a poisoned chalice.
"I look at Davina and she is just fantastic and encompasses everything that was Big Brother. No matter what happens there will always, always, always be comparisons made to Davina."
She continued: "In a sense I've been through that before with The Big Breakfast, which was actually my big break so I could never say anything bad about it. It was the most incredible experience and actually the best, most fun show - apart from Total Wipeout - that I've ever done.
"You take over from Johnny [Vaughan] and Denise [Van Outen] and you're drinking out of a poisoned chalice. Comparisons are always going to be made. I think it's not really the best situation to be in, but work is work. I'm calling my agent!"
> Byram offers Bleakley Daybreak support
> Click here to read our full chat with Amanda