Scotland's most capped hooker agreed a severance deal with Leeds after they were relegated from the Guinness Premiership.
Three other former Glasgow-based colleagues of Gordon have also ended their connection with Leeds - centre Andy Craig, breakaway forward Roland Reid and scrum-half Mark McMillan.
Gordon told The Scotsman: "It is very disappointing that things didn't work out at Headingley the way I imagined they would when I made the move from Glasgow last summer.
"At the moment, I have no idea what I will be doing in terms of rugby but I would not rule out anything, including a return to Scotland. I would, however, probably rule out the possibility of playing as a full-time professional again because I have the rest of my life to take into account now. I would be more likely to be willing to fill in for a team on a part-time basis."
Gordon added: "In the short-term, I will be taking a holiday with my wife Jenny and that will give me the chance to regroup.
"I have lots of options, including studying and doing more travelling. Jenny will also be due back at work in Glasgow after taking a few months' leave of absence to be with me in Yorkshire. The aim is to relax and make the most of the summer and then weigh up all the possibilities."
Borders coach Steve Bates could see Gordon as a short-term solution to his front-row problems, with Ross Ford likely to be out until well into next season.