Montgomery is a Celtic academy product and made his debut for the senior team last season, but broke through this term.
The young left-back has made 18 appearances for the Bhoys this term in all competitions, including four starts in the Europa League.
However, since mid-October game-time in the league for the starlet has dried up and the Hoops want to ensure the best possible development for the player.
Thus they are all set to send the young left-back on loan for the rest of the season in search of first-team opportunities.
Manager Ange Postecoglou is an admirer of the left-back and wants the player to get as much as game-time as he can.
He is hoping that the youngster comes back from his loan spell a much more-rounded player and starts challenging for the first-team places again next season.
It is believed that the Bhoys are looking at both clubs inside and outside Scotland as possible destinations for the youngster.