The 29-year-old didn’t make a single appearance for Celtic in 2019 and made just 16 league starts in his three year stint in Glasgow.
He’s out of contract at Celtic and will certainly not be offered a new deal by the champions.
Gamboa was offered a return to Costa Rica by 29-times champions Deportiva Alajuelense.
He left Costa Rica nine years ago, ironically after being rejected by Deportiva Alajuelense, where he had a trial.
But he opted to reject the chance of returning home in a bid to stay in Europe and has been targeted by Copenhagen, which could see him feature in next season’s Champions League.
He’s won 70 caps for his country, but failed to ever nail down a regular spot at Celtic, where he was usually back-up to Mikael Lustig, who also looks set to leave Glasgow this summer.
Gamboa has scored just one goal in his club career - for Norwegian club Fredrikstad eight years ago, but has netted three for his country.