Current right-back Glen Johnson is apparently unhappy at Anfield and looking for a move away. A ready made replacement would be Fanni of Rennes. The 29-year-old would be available for around £3m although Liverpool will face competition from Marseille for his signature, and possibly from a few other Premier League sides.
Liverpool could do with reinforcements at centre-back, particularly with Jamie Carragher currently out of the side with a serious injury. Stoke's Shawcross would be a solid reinforcement, and at 23-years-old, fits the bill of a player who would make a good investment. Stoke are unlikely to let him leave cheaply, although are rumoured to be looking at a back-up if he does move on. Tottenham and Manchester United (Shawcross' former club) could also be in the hunt.
Another option at centre-back is Shawcross' Stoke City team-mate Huth. The 26-year-old has been a regular fixture in the solid line of defence at the Britannia Stadium since he joined the club from Middlesbrough in 2009. The German, who has gone on record to say he's happy at Stoke, would reportedly command a fee of £5m.
This rumour has come from the players' ties with Liverpool's new director of football strategy Damien Comolli. The tough-tackling midfielder plays at Saint-Etienne, Comolli's former employers. Rated at around £7m, the 23-year-old made his international debut for France in 2010. Again, he's a player that fits the bill of a young, emerging talent - although Liverpool are likely to face stiff competition from some of Europe's top clubs if Saint-Etienne indicate the player can move on.
Aston Villa winger Young is interesting a few clubs during this window, most notably Tottenham Hotspur. Yet Liverpool are also said to be monitoring the situation. Aston Villa are adamant they won't sell - but in the cases of Gareth Barry and James Milner, they've shown that their head can be turned should a big offer be tabled.
Another player who could arrive at Anfield through Comolli's links is Lille midfielder Hazard. The 19-year-old Belgian has been instrumental in firing his team to the top of the league table in France and has already been watched by Hodgson and Kenny Dalglish this season. It's thought he could cost as much as £18m, although with the likes of Barcelona, Real Madrid and Chelsea showing interest, it's unsurprising.
Bolton's record signing Elmander has gone from a waste of money to one of the best players in the league following his performances this season. Yet the Swedish international is out of contract in the summer and Bolton may find themselves forced to cash in while they can. A sum as little as £5m could be enough to tempt the Trotters to let the 29-year-old leave.
Liverpool are apparently on the verge of making an £11m bid for Ivory Coast striker Gervinho. He's another player currently plying his trade at Lille, and any deal is likely to be smoothed by Comolli's contacts. The striker has been in fine form this season, hitting 11 goals for the French league leaders. With Fernando Torres in such woeful form - another striker will be top of Hodgson's wish list.
According to some stories in the press, Liverpool have already sent scouts to watch 27-year-old striker Aleksandr Kerzhakov in action for Russia. At club level he plays for Zenit St Petersburg, whom he rejoined in January of 2010 after an ill-fated spell at Sevilla and subsequently Dynamo Moscow. It's thought the 28-year-old would cost in the region of £6m.
Another player from France, and this time from Lyon. The Argentine is considered a natural goal scorer, but also a player with a strong work ethic and range of abilities. Rumours suggest Lyon are ready to let the 27-year-old leave and clubs are currently being sounded out. Although whether Liverpool's owners would be willing to fork out the £20m necessary to secure his services remains to be seen.
Roy Hodgson's time at Liverpool has seen him heralded as a stabilising factor, lambasted for a negative style of football and most recently forced to apologise to fans for questioning their support.
Injuries and a lack of form from Anfield's stars have hampered the Reds' progress this season, so some new faces seem likely in this January window.
The new American owners have made it clear they won't throw their money at the club, but if a signing has value, they will look to improve the squad.
So here, we take a look at the players who have recently been linked in the press and on the web with a move to Liverpool.