What has the manager said?
Liverpool manager Jurgen Klopp has said he is open to making signings in January, with the club "always ready" in the transfer market.
"We are pretty much always ready - if we can do something which helps us, we will try to do it. If not we will not."
Liverpool have already secured the signing of Takumi Minamino, who will join from Red Bull Salzburg on January 1.
What did Liverpool do in the summer?
It was a quiet summer for Liverpool, making just three signings. Adrian arrived on a free transfer while youngsters Harvey Elliott and Sepp van den Berg joined from Fulham and PEC Zwolle respectively.
Alberto Moreno and Daniel Sturridge were released - eventually joining Villarreal and Trabzonspor respectively - while Ryan Kent moved to Rangers on a permanent deal for £7.5m. Bobby Duncan also left for Fiorentina (£1.8m), Rafael Camacho joined Sporting Lisbon (£5m) while Harry Wilson made a loan move to Bournemouth.
Who have they been linked with?
Victor Osimhen, Lille [Sky Sports News]; Jadon Sancho, Borussia Dortmund [Daily Express]; Ryan Fraser, Bournemouth [TalkSport]; Mathieu Goncalves, Toulouse [Daily Mail].
Who could depart?
Rhian Brewster, Swansea [Sky Sports News], Nathaniel Clyne [Sky Sports News], Adam Lallana, PSG [Daily Mirror]; Harry Wilson, Bournemouth [TalkSport];
Analysis: What to expect this January
Sky Sports News Vinny O'Connor...
"Liverpool have wanted to sign a new versatile forward and it appears they have their man in Takumi Minamino from RB Salzburg for a seemingly bargain price of £7.25m.
"Other than that, the Reds are open to anything that can improve on what they have got, but with a Champions League-winning squad and one on course for a first Premier League title, that leaves their options very limited.
"In terms of outgoings, young striker Rhian Brewster is available for loan and there have been a number of inquiries already, including from Swansea in the Championship. Aston Villa are also keen.
"Nathaniel Clyne is also available again with his injury recovery close to completion and a return to training pencilled in for next month."
How to follow the January transfer window with Sky Sports
Sky Sports will bring you the very latest news from the January transfer market with the return of three shows.
Start your day with Good Morning Transfers at 9am as our team of reporters bring you the latest news and insight. Transfer Talk then follows at midday delivering analysis of the biggest stories. Then join us at 7pm for the definitive round-up of the day's news with The Transfer Show.
Meanwhile, the Transfer Talk podcast will also be back at the turn of the year with more expert analysis from here and across the continent.
And as well as tuning into Sky Sports News, don't miss a thing with our dedicated Transfer Centre blog.