Chelsea's Daniel Sturridge and Blackpool's Thomas Ince have been the most speculated names but three foreign players have been linked with the club across three different papers on Tuesday.
The Daily Mirror cites reports in Spain saying that the Reds could be keen on a move for Valencia winger Sofiane Feghouli.
The paper says that: "The Algerian wideman plays predominantly on the right, and would provide some depth to an already thin-looking squad."
Valencia are trying to extend Feghouli's contract, which expires in 2014, but are struggling financially, and may be forced into a sale.
The paper's Spanish corresponded David Cartlidge says that if Liverpool sign the 22-year-old they "would get a player who is hard working, direct, skilful and has a lot of potential. He can replicate Kuyt's success at the club."
Meanwhile, the Daily Mail says that another potential target is French centre-back Nicolas Isimat Mirin, another player who is out of contract in 18 months.
The 21-year-old is a regular for Valenciennes in Ligue 1 and is a French U21 international. Liverpool are targeting him because they believe first choice centre-half target - Feyenoord's Stefan de Vrij – could be too expensive.
Finally, the Daily Star says that the Reds have been put on 'red alert' by Atletico Madrid star Arda Turan, whose agent told the Turkish media that he is keen on a new challenge.
The Turkish left winger has been pictured in a Liverpool jersey in the past but looks the most unlikely of the three targets as his release clause of £19.5 million would appear to be too big for Liverpool.
The other transfers rumours, and a couple of England veterans could be set to leave the Premier League.
The Daily Mail reports that Frank Lampard is wanted by former Chelsea manager Claudio Ranieri at French second division side Monaco as the England midfielder prepares to quit Stamford Bridge.
Ranieri was the man that brought Lampard to Stamford Bridge and while Monaco could not match his current £130,000-a-week wage, they do have deep pockets, and could offer a tax free deal.
Also in the Mail is the news that Rio Ferdinand may choose to leave Manchester United in the summer despite the being likely to be offered a new one-year contract to stay.
Clubs in the USA and the Middle East are keen on Ferdinand and the paper says "it is understood that the veteran defender wants to see how his body copes with the rigours of the winter programme before making a decision."
Newcastle United are in advanced talks to sign France international striker Loic Remy for £10 million and hope to announce the deal at the start of the January window, according to the Daily Telegraph.
The move will also involve Remy’s current club, Marseille, signing a Newcastle player, possibly one of their Frenchmen such as Gabriel Obertan who could be surplus to requirements at St James’ Park.
Finally, Stoke and Aston Villa are leading the race to sign Crewe’s latest midfield starlet Luke Murphy. (Daily Mirror)