The Turkish Super Lig side are said to be pursuing a deal for the 27-year-old, who spent last season away from Anfield on two seperate loan spells.
Phillips spent the first half of the campaign at Scottish giants Celtic but only managed eight appearances for the Bhoys, with Liam Scales and Cameron Carter-Vickers remaining as the first-choice pairing in defence for Brendan Rodgers.
Seeking regular first-team action, the centre-back secured a temporary switch to Cardiff City in January, featuring in 18 matches for Erol Bulut's Bluebirds.
A serious injury sustained by Mark McGuinness paved the way for Phillips to become a starter in South Wales, where he formed a good partnership with Dimitrios Goutas.
Liverpool 'dismiss' Trabzonspor offer for Phillips
According to The Athletic, Liverpool have rejected the first offer of the summer transfer window for Phillips, who is set for a move away from Anfield.
It is said that Turkish Super Lig outfit Trabzonspor were the club to make an official approach for the defender, however the bid did not meet the Reds' demands.
The report claims that Liverpool value the 27-year-old at £8m and will not be hurried into a sale, despite the player being considerably low down the club's defensive pecking order.
Captain Virgil van Dijk, Ibrahima Konate and Joe Gomez all are undeniably ahead of Phillips in the Reds hierarchy, as too is Jarell Quansah, who enjoyed a breakthrough campaign in 2023-24 and is now on the fringes of Gareth Southgate's England squad.
Phillips revealed during an interview in April that he is expecting to leave the Merseysiders this summer, with one year remaining on his current terms.
Burnley to reunite Phillips and Scott Parker?
On top of interest from Trabzonspor, it is believed that Championship outfit Burnley are interested in the signing of Phillips ahead of the new season.
The Clarets are preparing for life back in the second tier of English football after suffering relegation from the Premier League under the stewardship of Vincent Kompany.
With the former Manchester City captain departing Turf Moor to occupy the managerial hotseat at Bayern Munich, Burnley have appointed Scott Parker to lead the Lancashire club's attempts to return to the top flight at the first time of asking.
The 43-year-old has managed Phillips previously during the second part of the 2021-22 campaign, when Phillips was on loan at Bournemouth in the second tier.