Caulker still has one year remaining on his existing deal at Loftus Road, but the Championship outfit will not stand in his way if he receives a suitable offer this summer.
The 25-year-old has previously revealed that he has been battling depression and has not made a first-team appearance for QPR since October, but according to The Mirror, Celtic boss Brendan Rodgers is ready to take him to Glasgow.
Rodgers has worked with the centre-back at both Swansea City and Liverpool, and it appears that he sees the England international as another option at the back.
Caulker has already played for eight clubs during his career, and Celtic would likely keep any offer to 12 months should they press on with the transfer.
On two occasions in 2013 and 2014, Caulker cost £8m, but he has spent two periods on loan since signing for QPR in 2014.