Posh chief Barry Fry has revealed they've now accepted a bid from Leicester City for the Scotland international.
"We have accepted a bid from Leicester," said Fry in the Leicester Mercury.
"Their manager Sven Goran Eriksson is out of the country at the moment, but was due to speak to Craig over the weekend.
"I have had several conversations with West Ham, but we have turned down their bid. I am certain they will be back.
"Craig is facing a tough decision. He turned down Norwich and he has now turned down QPR."