The Merseysiders want to quickly conclude an agreement until the end of the season with QPR for the 24-year-old, who could train under Jurgen Klopp for the first time in the club’s late afternoon session if formalities are finalised.
For Caulker to be eligible for Wednesday’s Premier League visit of Arsenal, he would need to be registered by noon on Tuesday.
The clubs are trying to complete the paperwork, which would be subject to a medical.
Kolo Toure is the only centre-back currently guaranteed to be available for the encounter at Anfield, while Mamadou Sakho is pushing to be included after shaking off a minor knee injury.
Klopp paused the search for defensive cover as he monitored the France international’s return to training, but given the unrelenting fixture schedule, he has decided it was not worth the risk to ignore a possible option.
Dejan Lovren’s recovery from a hamstring problem is progressing faster than anticipated, but Klopp wants to alleviate the strain on his centre-backs by signing another defender, with Martin Skrtel also still sidelined.
Caulker, who joined Southampton on a season-long loan at the end of July 2015, failed to regularly secure minutes under Ronald Koeman. He only made eight appearances in the first half of the campaign, the last of which came in December when Liverpool smashed Saints 6-1 on the south coast.
That lack of game time has encouraged QPR to cancel the agreement and discuss a move to Merseyside for the former Tottenham man on temporary terms.
READ MORE | LIVERPOOL'S JANUARY HITS AND MISSES
The negotiation is proving to be the least problematic for Liverpool, with Borussia Dortmund blocking a move for Neven Subotic.
Inter’s Andrea Ranocchia, who has been courted by Sampdoria and Bologna, was also looked at while Schalke’s Joel Matip did not want to depart in the winter window.
Caulker would be eligible to play in the Europa League if Liverpool opt to register him. He will be also be available for FA Cup encounters should the Reds get past Exeter City in the third round replay, which he cannot feature in due to not being registered for the original tie.
Former Liverpool boss Brendan Rodgers previously wanted to secure the services of Caulker, whom he managed at Swansea.