West Ham have also been linked with a move for the defender for some time.
Phillips has featured on only three occasions this season – including a Champions League start against AC Milan at San Siro – due to the return to fitness of Virgil van Dijk, Joel Matip and Joe Gomez and the summer arrival of Ibrahima Konate.
However, he played an integral part in the club’s late run to third place last season when injuries left Liverpool without their three senior central defenders.
The club will not sell Phillips on the cheap but, with the players in front of him and the interest being expressed, the PA news agency understands it is increasingly likely he will move before Monday’s deadline.
Fellow centre-back Rhys Williams, who last week was recalled from a loan spell at Swansea due to a lack of game time, is wanted on loan by Sheffield United but fellow Sky Bet Championship side Reading are also believed to be interested.
Liverpool are looking for certain assurances over playing time after the 20-year-old’s Swans experience, however, his immediate future is linked to Phillips.
Williams was initially recalled on the assumption the more senior centre-back would be leaving, so if that does happen the club will assess whether the youngster will be allowed to go back out on loan.
Liverpool are hopeful they can secure a loan with an obligation to buy deal for the right-back, who has made eight appearances this season, two of which were Champions League starts against Porto and AC Milan.
Midfielder Leighton Clarkson, another youngster recalled early from a spell at Blackburn, will not be going out on loan again in January.