We may be well into the Premier League season, but teams never stop looking to improve, and rumours surrounding Liverpool and their transfer targets are still rife a month after the summer transfer window shut.

In September, there were a number of players linked with Brendan Rodgers' men. The Reds might make moves for some of them in January.

Here are the top four.

4. Igor Denisov

Igor Denisov has been demoted to the youth team at his Zenit St Petersburg alongside striker Alexander Kerzhakov after criticizing his club's transfer policy. According to talkSPORT, Liverpool will be among the clubs set to fight it out for the 28-year-old midfielder.

When Liverpool's stalwart defensive midfielder Lucas Leiva fell victim to a long-term injury last year, the Reds were left with a major hole in the team with no capable replacements.

That could be fixed with the signing of the Russia captain.

If Denisov has not repaired his relationship with Zenit by January, Brendan Rodgers could well pounce and pick up another talented midfielder at what would be a discount rate.

3. Theo Walcott

Liverpool chased Arsenal winger Theo Walcott all summer, and according to the Daily Mail, that interest will be reignited in January with Walcott yet to sign a new contract at the Emirates Stadium.

The England international, who has scored 27 goals over the past three seasons, is reluctant to sign a new deal unless he is promised the opportunity to play up front. With Liverpool's desperate need for strikers, Walcott-to-Liverpool could be a match made in heaven.

Walcott would be a nice addition to the Reds frontline, and he would add great speed to complement the skill and strength of Fabio Borini and Luis Suarez. If he has not signed a contract in January, he'd be available very cheaply and would be well worth a bid for Brendan Rodgers.

2. Isco

For years now, the Reds have been looking to pick up a long-term replacement for captain Steven Gerrard. According to AS, the search might have led to Spain, and Malaga's Isco.

The 20-year-old Spaniard is one of the most promising midfielders in Europe, having broken through last season with his club, and he appears to be ready to step up in his career.

A dynamic midfielder, Isco would be a sensational pickup for Liverpool. Developing quickly, he could be one of the continent's better players in a few years' time.

Liverpool could make a bid in January. 

1. Marc-Andre ter Stegen

Rapidly emerging as one of Europe's better goalkeepers, Marc-Andre ter Stegen is ready to move on from Borussia Monchengladbach and, according to Metro, the 20-year-old could be in line for a move to Anfield.

Liverpool's long-time goalie Pepe Reina has struggled to start the season, conceding 12 goals through six Premier League games and making numerous mistakes along the way.

Form is temporary, but class is permanent, and Reina should turn it around. But if he doesn't, ter Stegen would be a wonderful signing for the Reds. 

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