Manager Jurgen Klopp currently has Martin Skrtel and Dejan Lovren sidelined by hamstring injuries and although fellow centre-backs Kolo Toure (cramp) and Mamadou Sakho (knee) both look likely to be fit for Thursday's visit of Arsenal, the German feels he needs more cover.
An enquiry has reportedly been made to the Championship club for the defender, who is currently on loan at Southampton.
Caulker has made just eight appearances for the south-coast club - the last of which came against Liverpool in last month's 6-1 Capital One Cup quarter-final defeat - but only one of those has been a Premier League start back in August.
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On that basis Liverpool hope QPR can cancel his loan deal in order for them to bring the 24-year-old to Merseyside.
Liverpool's scouting department are more than familiar with the former Tottenham centre-back as he was a target for previous manager Brendan Rodgers.
Borussia Dortmund's Neven Subotic was on the list of names of potential centre-back cover as he too has struggled for pitch time this season but the Bundesliga club's boss Thomas Tuchel has ruled out that possibility.
