The 32-year-old is out of contract at the end of the campaign and could be set to move on with County looking likely to fall out of the top flight.
The Highland side are two points adrift at the bottom of the table with one game left to play.
Dundee United are also in the hunt for the ex-Celtic youngster. Gardyne spent three years at Tannadice between 2012 and 2015, though that included loan spells with Kilmarnock and County.
It is believed the player would prefer to return to United, though that would depend on which division the club are playing in next season.
Csaba Laszlo’s side trail Livingston 3-2 going into the second leg of their Scottish Premiership semi-final.