The Costa Rican international has been out of the picture this season, playing just seven times in all competitions with the last coming in December.
Gamboa, a £1 million signing under previous manager Brendan Rodgers in 2016, is out of contract at Celtic Park next month and it would be no surprise if the 29-year-old left the club over the summer.
His wife Melissa posted a series of pictures on Instagram, including one showing Gamboa with Hoops colleagues Nir Bitton, Dedryck Boyata, Dorus De Vries, Jonny Hayes and Tom Rogic, with the caption: "How lucky I am to have something that makes saying goodbye so hard!"
The former Rosenborg full-back has played 25 times in total for Celtic, with 19 coming in the Scottish Premiership.His last outing for Celtic was in the 1-1 draw with Motherwell at Fir Park on December 5. He also featured against Rosenborg, Suduva and RB Leipzig in European matches.