Pym was effectively placed on the transfer list 10 months ago after falling out with former Posh boss Darren Ferguson. A change of manager to Grant McCann made no difference to Pym’s future and he has been given permission to talk to four League Two clubs.
Mansfield – currently 10-1 fourth favourites for the League Two title – are one of those and Field Mill is Pym’s preferred destination.
But the Stags have yet to come up with a deal agreeable to Posh.
Posh director of football Barry Fry said: “Mansfield want Christy and he has spoken to them along with three others clubs. He wants to go there, but Mansfield have yet to come up with an offer that suits us.
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"Their manager Nigel Clough is due back from holiday this week so things might move on then.”
Posh want a fee for 27 year-old Pym even though he is surplus to requirements. He was one of several League One promotion winners to sign extended contracts at the Weston Homes Stadium last summer.
Posh have signed two goalkeepers on loan for the season, Harvey Cartwright from Hull City and Lucas Bergstrom from Chelsea.