The 29-year-old Greece international, who joined the Hoops in 2008, will be out of contract at the end of the season.
Despite failing to agree new terms with the Scottish champions, Samaras has suggested that he wants to stay at Parkhead.
"When I started playing football, I always wanted to stay at a club for many years. I didn't want to change clubs like other players do, moving every two or three years," he told Celtic's official website.
"I wanted to love a club and for it to love me back, so they could remember me for something. This club for me is Celtic.
"I have tried my best and tried to help my team mates be successful, but the most important thing is that it's good for me to know that I have a connection at the club and that's really important. I am not a passenger."
Samaras has won four Scottish Premierships, two Scottish Cups and the Scottish League Cup during his time with Celtic.