Everton and QPR are also interested in the Scotland international.
The Hammers have also been linked with Mackail-Smith's Posh team-mate Joe Lewis, but Fry insists he has not spoken to them regards Lewis and that Mackail-Smith is the only player West Ham have expressed an interest in.
"West Ham have not spoken to me about Joe Lewis," said Fry.
"But they did ask me what we wanted for Craig. They have not made a bid as yet, but they are having a serious go at getting back into the Premier League straight away.
"One Premier League club who have spoken to Craig set him a deadline of today to make his mind up, but he will not be going there. It's not a question of money, it's a couple of other things that he's not happy about.
"Craig is right not to rush into anything because there is still plenty of interest in him."