The centre-back played under Bhoys boss Brendan Rodgers at Swansea City.
Caulker struggled for game time last season
Caulker, who played under Bhoys boss Brendan Rodgers on loan at Swansea City, recently returned to Loftus Road following temporary stints at both Southampton and Liverpool.
Hasselbaink says he doesn't want to lose Caulker
However, his reported £30,000-a-week wages are said to be a burden on the Championship side's finances, after they failed to gain promotion to the Premier League last season, and he could me moved on following the capture of Joel Lynch this week.
Celtic are said to be on the lookout for a new centre-half, with Dedryck Boyata injured, Tyler Blackett back at Manchester United and Charlie Mulgrew out of contract and still to commit.
Mulgrew's future is uncertain
Ex-Liverpool man Kolo Toure (the Daily Mail) and Blackburn Rovers'
Duffy was linked with a move to Celtic this week
Ireland international Shane Duffy (also the Daily Mail) are two of the names being linked with moves to Parkhead.