The 36-year-old has been with The Cobblers since 2005 but says his future is elsewhere after meeting with manager Stuart Gray.
"The manager has looked towards next season and he sat me down on Friday and explained to me what he was going to do," Jess told the Northampton Chronicle.
"My contract was up in the summer anyway, so it was just a matter of being released. There's no bitterness, not at all. The manager has made a decision and I've got to respect that.
"I suppose I'm disappointed with the way it's panned out but I've been in the game long enough and I'm old enough to handle it."
However, Northampton insist a final decision on Jess' future has not been made and that discussions are ongoing.
"Northampton Town Football Club are aware of media reports concerning the future of Eoin Jess," a statement read.
"The club are in consultations with Eoin and when these discussions have been finalised, a formal announcement will be made.
"That position has not yet been reached despite media reports."
Sky Sports