The Championship new boys are prepared to let the striker leave London Road over the summer and there are a string of clubs chasing Mackail-Smith.
Fry claims the Scotland international has already turned down moves to Premier League duo Norwich City and Queens Park Rangers, while West Ham United have seen an offer rejected.
Posh expect the Hammers to return with another bid, while Fry is waiting to learn the outcome of Mackail-Smith's impending talks with Leicester boss Sven-Goran Eriksson.
"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."