Shane Duff has rejected the offer of fresh terms at Cheltenham Town, but remains in talks with the club.
The 29-year-old defender enjoyed his testimonial year at Whaddon Road last season after 10 years of loyal service.
He was, however, troubled by injury throughout the course of the campaign and was unable to play as integral a role in first-team affairs as he would have hoped.
Duff is now pondering whether the time has come for him to take on a fresh challenge, with an enticing offer from outside England believed to be on the table.
Spurning the latest offer put to him by Cheltenham suggests he could be about to sever ties with the club, but manager Mark Yates insists an exit is not inevitable and has vowed to do all he can to talk the centre-half round.
The Robins boss told the club's official website: "Shane has been a great servant to this football club so we talked and I put an offer of a new contract on the table for him. We had to put a deadline on it in the end but Shane's agent contacted me on Friday at 5pm to let me know that he was turning the offer down.
"We're still talking to Shane and the door hasn't closed yet but we need to be looking at other options and preparing ourselves for next season."
Meanwhile, youngsters Theo Lewis, Kyle Haynes, Jake Lee and Josh Emery are set to sign professional contracts with the club after being offered deals towards the end of last season.