The former Newcastle United man has so far failed to live up to his £35 million price tag - should new Anfield boss Brendan Rodgers move the England international on?
The forward has had a poor first 18 months at Anfield and has struggled to recapture the form he showed at Newcastle United that persuaded the Reds to part with £35 million.
In 20 games for the Magpies during the 2010-11 campaign before his January 2011 switch, he had scored 11 times.
Since moving to Merseyside, the striker has scored the same amount of goals, but in a much less economical 56 appearances.
However, the silver lining for the 23-year-old was that he was selected as part of the England squad for Euro 2012 by new Three Lions boss Roy Hodgson after a late spurt of solid performances in a Liverpool shirt.
One of the key decisions Rodgers will need to make early in his tenure is what to do with Carroll, and loaning him out to a club that is more likely to start him every league match could be of benefit to both the coach and striker.
On the other hand, many Reds fans will want to see him starting more frequently this season; contrastingly, some supporters will be keen to show him the door as soon as possible.
What do you believe Liverpool should do with their Carroll conundrum? Should he be chosen as a key cog in Rodgers' line-up? Should the former Swansea City coach deploy him more as an impact substitute this season? Will a loan be the most beneficial option for all parties concerned? Or should the Reds cash-in on the striker if a decent enough offer arises?
Let us know your opinion by voting in the poll, adding your suggestions in the comments section and getting involved in the debate on Facebook and Twitter.