Stockport have made bids for Ryan Lowe, Jamie Vardy, and Sean McConville, BBC Radio Manchester understands.
Bury striker Lowe, 32, scored 28 goals as the Shakers were promoted from League Two last season.
Accrington Stanley midfielder McConville, 22, will train with the club with a view to a possible move.
FC Halifax Town striker Jamie Vardy scored 23 goals in 14 starts last year as the club were crowned champions of the Evo-Stick Northern Premier League.
Veteran Lowe has said he feels Bury should reward him for his part in their promotion campaign by extending his current deal, which has two years still to run.
In a statement Bury said they had received an offer from an 'un-named club', but described the bid as 'totally derisory'.
McConville was sent off as Accrington's season ended in a 3-0 aggregate defeat by Stevenage in the League Two play-off semi-final.
The three offers come a day after Liverpool-based businessman Tony Evans became a director at the club, in anticipation of a proposed takeover by the consortium he leads.