The Costa Rican international has barely featured for the Hoops this season.
Gamboa signed for the Scottish club back in 2016 and has failed to live up to expectations.
The 29-year-old has earned 70 international caps for his country and was part of the 2014 FIFA World Cup squad.
The centre-back was also part of the side that won the CONCACAF U-20 Championship in 2009.
Gamboa commenced his career with his country’s club Municipal Liberia, where he made 68 appearances.
He also had short spells at Copenhagen, Rosenberg and Fredrikstad.
His contract is due to expire later this season and the Hoops are having no second thoughts about the defender’s contract extension.
Gamboa is wanted by the 29 times Costa Rican champions Alajuelense, with whom he earlier had a trial.
Neil Lennon, the interim manager has made a great impact at Park Head since taking charge.
He led the Bhoys to six wins and is yet to face a defeat. The major victories include the Old Firm derby win, followed by the Scottish Cup semi-final domination against Aberdeen.
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They are in pole position to clinch the Premiership title for the eighth time in a row and possibilities are high for a domestic treble as well.