Brendan Rodgers
Liverpool boss Brendan Rodgers is aware of his club's shortage of options up front. Reuters

Having allowed Andy Carroll to leave on-loan to West Ham last week, the expectation was that Liverpool would be signing a replacement before the close of the transfer window. However, Friday's deadline came and went without a goal-scorer being signed. Fulham rejected offers for Clint Dempsey, while a loan move for Daniel Sturridge also fell through to leave Luis Suarez and Fabio Borini as the only established forwards at Anfield.

Sunday's defeat to Arsenal on Sunday demonstrated Liverpool's lack of a cutting edge, leading manager Brendan Rodgers to state that he would consider a move for a free agent rather than merely wait until the transfer window reopens in January.

"Any player I believe can improve the squad I will look at," Rodgers said, according Liverpool's website. "We've got a very small group, 19 players training yesterday morning, and some very young players in and amongst that. I can't say no, I always have to look and see where we can improve the group."

Liverpool have already failed in a late move for Alessandro Del Piero, who instead honored his agreement to join Sydney FC, while former Red Michael Owen has joined Stoke City. Here are five players that Liverpool could still look to recruit.

Didier Drogba
The former Chelsea powerhouse may not yet be a free agent, but speculation continues that he soon may be. Drogba moved to Chinese side Shanghai Shenhua following his departure from Stamford Bridge this summer, signing a deal worth a reported £200,000 a week. Yet that bumper contract could be in jeopardy as a result of a dispute between the club's shareholders.

If that does happen then the Ivorian would be one of the most sought after free transfers around. He may be 34 and would command another hefty wage packet, but Drogba showed last season that on his day he remains an intimidating prospect for opposition defenders. His style wouldn't exactly fit seamlessly with that of Rodgers' approach, but, with Liverpool so short of options up front, Drogba could be an exciting addition.

Nicolas Anelka
Like his teammate in China, Drogba, Anelka's massive contract could soon be compromised due to behind-the-scenes events at Shanghai Shenhua. At 33, the former France international should still be capable of making a contribution at Premier League level, despite having last played in England for Chelsea last November.

Anelka would also be in familiar surroundings at Anfield, having played for the club during a loan spell in the second half of the 2001-02 season. A largely successful period on Merseyside means that Anelka would also be likely to receive a warm reception from the Liverpool faithful. Could Anelka's much-traveled career have a final splash at Anfield?

Emile Heskey
The signing of Heskey truly would be a last resort, arguably for any Premier League club, let alone one of Liverpool's standing. The 34-year-old has been a free agent since leaving Aston Villas this summer, having scored a dismal nine goals in three and a half years at the Midlands club.

The hulking frontman spent four years at Anfield earlier in his career, but a lack of goals that has blighted his career eventually persuaded Liverpool to dispense with the former England international. It truly would be an incredible story were Heskey to return to Liverpool, eight years after he was sold to Birmingham City.

Eidur Gudjohnsen
Another former Chelsea forward, Gudjohnsen has been without a club since being released by Greek side AEK Athens. The technically-gifted former Iceland international has had a nomadic career since leaving Barcelona in 2009, enjoying short spells in the Premier League with Tottenham, Stoke and Fulham, as well as in France with Monaco.

His recent record suggests that he would make a limited impact at Liverpool and it would be a shock should Rodgers turn to the 33-year-old for reinforcement. Latest reports suggest that Gudjohnsen could be set for a move to Major League Soccer with the Seattle Sounders.

John Carew
The physically-imposing Norwegian left West Ham in the summer after one season with the Hammers. The 33-year-old has rarely been a prolific scorer throughout his career, but enjoyed some impressive form during the initial stages of his four-year spell with Aston Villa.

His playing style coupled with a tendency for off-the-pitch drama means he is a long-shot to sign for Liverpool, especially with speculation linking him with a move to Celtic.