The 27-year-old has largely impressed since making the move to Glasgow in 2015 under former manager Mark Warburton.
Though he recently signed a new deal until 2020, Rangers wish to use such leverage to secure a sizeable transfer fee for the player, which they can then reinvest in other parts of the squad.
The ex-Swindon Town stopper could well have played his last game for the club with an injury poised to keep him out of Sunday’s Old Firm clash with Celtic and possibly the rest of the campaign.
Deputy Jak Alnwick is set to remain in goal after deputising for Foderingham during the 2-1 victory over Hearts this past weekend.
Rangers already look to have a replacement lined up with a deal for Allan McGregor set to be completed in the coming days.