Branston, the former Rotherham star, is well down the pecking order at Hillsborough and is set to be released - if Wednesday give him a decent offer to terminate his contract.
Chris Turner signed the player on a Bosman in the summer on a two-year deal but it has been clear from day one that Paul Sturrock does not see him fitting into his plans.
Fry, who has had Branston on loan twice at London Road is watching the situation closely and knows that the player will welcome a move away from S6 in a bid to play first-team football.
He told Peterborough's official website: "I will find out about Guy's situation on Wednesday because we are in action against Sheffield Wednesday up at Hillsborough - I will talk to Paul Sturrock and Guy and try to get something resolved.
"Sheffield Wednesday have made Guy what I would call a 'good offer', but Guy doesn't agree and is not going to accept it and if that is the case then there is nothing I can do about it. There is a possibility of Guy coming back here on loan, but Guy wants to get his future sorted out, which I can understand."