Mackail-Smith is one of the most sought-after players in this summer's transfer market, with Peterborough resigned to losing the highly-rated forward.
A number of Premier League clubs have been credited with an interest in the Scotland international, but West Ham have now expressed an interest in the 27-year-old.
The Hammers have been credited with an interest in 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."