The striker failed to make the 18-man squad that travelled to Bury on Saturday, with YTS pairing Stef Frost and Bobby Wilson both being preferred to the 26-year-old.
Gordon has not appeared for the Magpies since the 0-0 draw at Maccesfield, a game in which he received a barrage of abuse from the travelling Notts support - who ironically cheered when he was substituted.
"Gavin is available (for transfer) now," Thordarson told the Official Website.
"At this moment I don't see him fitting into my future team that I am trying to put together.
"I will not rule out anything in terms of moving people in or out, I am always looking for options to strengthen my squad and we have circulated Gavin's name to clubs and we will see where we go from there.
"Gavin is not likely to play regular football here and I have always said that I will not stand in the way of a player who has the chance to play football on a regular basis."
Gordon - whose real name is Kenyatta - was signed by former boss Gary Mills in the summer of 2004, having been released by Cardiff City.
Despite enduring criticism throughout his Notts career, the striker managed to find the net eight times last season, before his season ended prematurely in February due to a badly broken jaw.
The Manchester-born striker is believed to be one of the high-earners at Meadow Lane and now becomes the third player under contract, after Tony Scully and Matty Williams, who Thordarson has told to leave.