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What you need to know:
- While Eriksen is seemingly on the way out, Mourinho must focus on defensive reinforcements and Napoli's Elseid Hysaj, Marseille's Hiroki Sakai, Bournemouth's Nathan Ake and West Ham's Issa Diop are said to be on his shopping list.
- With second placed Leicester flying high, Brendan Rodgers maintains nobody will be leaving despite plenty of interest in his talented squad.
- Rodgers is on the lookout for fresh faces, with Juventus defender Merih Demiral and AC Milan's Hakan Calhanoglu potential targets.
The Premier League's January sales are open for business as clubs rush to snap up new year bargains in the one-month transfer window.
Liverpool are running away with the title race and have already signed Japanese star Takumi Minamino, so the Reds are likely to sit out the frenzy while the chasing pack try to make the additions that could help them close the gap.
Here, AFP Sport looks at the key transfer issues to address for the teams hoping to hang onto Liverpool's coat-tails:
Chelsea boss Frank Lampard is expected to make a big splash after being unable to sign players in the summer window due to the club's transfer ban.
With that two-window suspension halved by the Court of Arbitration for Sport, Lampard needs several new recruits to help accelerate the development of his promising young team.
Armed with a reported £150 million transfer war-chest, Lampard will look to improve at left-back, where Emerson and Marcos Alonso have been too inconsistent.
The Blues have already been linked with Leicester's Ben Chilwell to fill that role, but Lampard might not be satisfied with only one signing.
Having constantly bemoaned Chelsea's lack of cutting edge against defensive opponents, the Chelsea boss needs pace on the flanks, a clinical finisher to dove-tail with Tammy Abraham and, ideally, a creative midfielder.
Crystal Palace forward Wilfried Zaha, Leipzig striker Timo Werner and Lyon forward Moussa Dembele are among Lampard's mooted targets.
Ole Gunnar Solskjaer has revealed Manchester United are "looking at one or two" players after learning Paul Pogba will be absent for the next month.
France midfielder Pogba has been advised to undergo surgery on his ankle and that is a problem for United manager Solskjaer, who is already without Scott McTominay due to a knee injury.
"Of course it is playing on our decision making when we have two players out - Paul for a month and Scott for two," Solskjaer said.
"If it's available and if it's possible we will do something, definitely."
Solskjaer missed out on promising striker Erling Braut Haaland, who has signed for Borussia Dortmund from Red Bull Salzburg.
Aston Villa midfielder Jack Grealish, Leicester duo Ricardo Pereira and James Maddison, as well as Dortmund's Jadon Sancho have all seen their names connected to Old Trafford.
Mikel Arteta admits Arsenal could be more active than expected after Calum Chambers had surgery on a knee injury that will rule him out for a lengthy period.
It leaves new Gunners boss Arteta short of options in defence and he will meet with technical director Edu and head of football Raul Sanllehi this week to mull over their plans.
"We will try to be in the market to see options that can strengthen the team, that's for sure and our obligation and we will be working on that," Arteta said.
"My obligation is to give my opinion on the things we can improve. Obviously we have a bad injury with Calum a few days ago that will change our plans at the back."
Arteta, who must also focus on persuading Pierre-Emerick Aubameyang to extend a contract which expires at the end of next season, has been linked with bids for Leicester midfielder Wilfred Ndidi, Atletico Madrid winger Thomas Lemar and Leipzig defender Dayot Upamecano.
Manchester City are trailing 11 points behind Liverpool, so a January spree might not be worthwhile for the champions.
Pep Guardiola insists City will not rush into the January market because the quality of player available is generally not as high as in the summer window.
But City did sign Aymeric Laporte in the 2018 winter market, so a surprise swoop isn't out of the question, especially if the signing can help in Guardiola's quest to win the Champions League for the first time since 2011.
For Tottenham boss Jose Mourinho, the future of unsettled playmaker Christian Eriksen needs resolving as the Dane nears the end of his contract.
While Eriksen is seemingly on the way out, Mourinho must focus on defensive reinforcements and Napoli's Elseid Hysaj, Marseille's Hiroki Sakai, Bournemouth's Nathan Ake and West Ham's Issa Diop are said to be on his shopping list.
With second placed Leicester flying high, Brendan Rodgers maintains nobody will be leaving despite plenty of interest in his talented squad.
Rodgers is on the lookout for fresh faces, with Juventus defender Merih Demiral and AC Milan's Hakan Calhanoglu potential targets.