What's the latest on Alexander-Arnold, and others who might move?
The January transfer window is a notoriously tricky time to do business.
But a packed fixture schedule, injuries, keeping up a title charge or fighting to stay up means several Premier League managers have hinted that they will need to go into the market this winter.
The January transfer window for English clubs opened on Wednesday, January 1 and closes on Monday, 3 February at 23:00 GMT.
BBC Sport has taken a closer look at five high-profile players whose futures are likely to come under scrutiny over the next month.
Trent Alexander-Arnold (Liverpool)
Sources said on New Year's Eve there had been an approach - but no offer - from Real Madrid about signing Alexander-Arnold in January, which Liverpool rebuffed.
Spanish media also reported Real were willing to buy the England international this month.
Alexander-Arnold is one of three key Liverpool players in the final six months of his contract.
While Mohamed Salah and Virgil van Dijk have reluctantly provided snippets in interviews about contract talks it has been slim pickings from the England international.
He said in September that negotiations over a new deal would not be played out in public, which has added a cloud of uncertainty over what lies in store for the versatile 26-year-old, who has been at Liverpool since the age of six.
With Liverpool favourites to win the Premier League, looking good in the Champions League and in the semi-finals of the Carabao Cup, Real's overtures might be resisted for now - but how long will that last?
Contracted until: June 2025.
Linked with: Real Madrid, Manchester City.
Marcus Rashford (Man Utd)
It currently feels like a case of when Marcus Rashford will leave Manchester United, rather than if he will. The 27-year-old forward said in an interview in mid-December that he is "ready for a new challenge" amid uncertainty over his Old Trafford future.
Rashford has scored 138 goals in 426 appearances for the club since making his debut in 2016, having come through the United youth ranks. The 2022-23 campaign was his most prolific when he scored 30 in all competitions.
However, he has struggled for form over the past 18 months and attracted criticism from pundits and fans for a number of laboured displays. Rashford is one of United's highest earners which could be barrier to any move in January.
Contracted until: June 2028.
Linked with: Paris St-Germain, Barcelona and Saudi Pro-League clubs Al-Ahli, Al-Ittihad and Al-Qadsiah
Martin Zubimendi (Real Sociedad)
A top-class number six is like gold dust which explains why Real Sociedad midfielder Martin Zubimendi will be one of the hottest properties in January.
Liverpool were close to signing the 25-year-old in the last window after a drawn-out pursuit only for the Basque club to talk him into staying. The absence of Rodri at Manchester City has left them short of options in the position.
Zubimendi, who helped Spain win Euro 2024, reportedly has a £51.7m release clause in his contract. "I'm happy with the way I'm handling it," Zubimendi said of the ongoing speculation over his future before the transfer window. With Sociedad in mid-table he is not likely to be short of offers.
Contracted until: June 2027
Linked with: Liverpool, Arsenal, Manchester City, Barcelona
Ben Chilwell (Chelsea)
At 28 Ben Chilwell should be in the prime of his career at Chelsea but has instead found himself largely frozen out of he first-team picture at Stamford Bridge by boss Enzo Maresca.
Chilwell, who joined Chelsea for £45m from Leicester in 2020, has just 45 minutes of a Carabao Cup tie against Barrow to his name this season and having failed to get a move away from the club in the last window.
Maresca said Chilwell was among the players "thinking to leave" and the club will "try to find a solution" depending on what offers materialise for the left-back, who has won 21 caps for England. His wages seem to make a loan move most likely.
Contracted until: June 2027
Linked with: Juventus, Brentford, Manchester United, West Ham, Fenerbahce
Matheus Cunha (Wolves)
An electrifying start to the 2024-25 season has seen Matheus Cunha thrust into the limelight during what has largely been a season of struggle for Wolves.
Cunha has been involved in 11 goals in his past 11 Premier League appearances, scoring seven and assisting four. He is also the first Wolves player to score as many as 16 top-flight goals in a calendar year since John Richards netted 18 in 1980.
The Brazilian, 25, signed from Atletico Madrid in a deal which could be worth £35m which leaves Wolves with a dilemma: cash in for a substantial profit when the market is in their favour, or hang on to a player who has the capacity to keep them up.
Contracted until: June 2027
Linked with: Liverpool, Arsenal, Manchester City, Manchester United and Newcastle
Who else could be on the move in January?
Chelsea boss Maresca said Carney Chukwuemeka is for sale and a loan deal is being sought for fellow midfielder Cesare Casadei.
Barcelona's failed attempt to register Spain forward Dani Olmo has cast doubt on his future with the La Liga club.
Newcastle striker Alexander Isak has been regularly linked with Arsenal.
Bayer Leverkusen's Florian Wirtz and Newcastle's Bruno Guimaraes have both been linked with Manchester City.
January will be Manchester United boss Ruben Amorim's first transfer window in charge and he may want to bring in a couple of players to put his stamp on the side.
Sporting striker Viktor Gyokeres worked with Amorim in Portugal and has also been linked with Arsenal as well as a move to United.
Dutch striker Joshua Zirkzee and winger Antony are among those linked with the Old Trafford exit door.
Lille forward Jonathan David is out of contract at the end of the season and has been mentioned in connection with several Premier League clubs.
Paris St-Germain forward Randal Kolo Muani has also seemingly been linked with every club under the sun.
Tottenham may be forced into the window with defenders Micky van de Ven and Cristian Romero both sidelined with injury.
Crystal Palace are in the market for a goalscorer along with Everton, who have scored only 15 league goals, fewer than any team apart from Southampton.
