Nurses reports that the 25-year-old has already held talks with the club and that Brendan Rodgers is willing to give him a chance to revive his stuttering career.
After Dedryck Boyata suffered a knee injury ruling him out of action for up to three months, the Hoops could move to shore up any possible shortage of defenders.
Rodgers worked with Caluker at Swansea back in the 2011/12 season when he took him on loan from Tottenham and, after the player went public about his battles with depression, drinking and gambling, the Celtic boss is apparently willing to help him get his career back on track.
QPR are hoping to get Caulker off their wage bill as he is one of the club’s highest earners and they’ve let him behind in London as they’ve gone on their pre-season tour.
Caulker was close to joining Lokomotiv Moscow earlier this year but he pulled out of the move at the last second and it looks like could now be on his way to Celtic instead.