Carroll, who has been linked with both the London club and his former side Newcastle United, has seen his dream start to his Premier League career turn into a nightmare at Liverpool resulting in the out of favor striker being deemed surplus to requirements by the club that signed him for £35 million just 18 months ago.
The Mirror Sport have reportedly heard that The Hammers have put in a loan bid for Carroll for the coming season with a guaranteed £17 million being owed to Liverpool at the end of the season to make the move permanent.
Carroll impressed in the first half of the season in the Premier League wearing the the black and white stripes of his hometown of Newcastle. His 11 goals in 19 games caught the eye of Liverpool, who brought the 6'3" striker, in what many thought was a panic buy, on the last day of the 2011 January transfer window.
Since the move, though, Carroll has faced plenty of criticism for his performances for the Reds after failing to make the same headway in the league as he did in the north east.
After scoring just six goals in 43 league appearances and being out-classed in the forward position by Luis Suarez, new boss Brendan Rogers is happy to let the club's largest transfer fee move to new pastures.
With only a few clubs showing interest, it now seems that Sam Allardyce's Hammers want to lead the charge to sign the towering striker and are hoping that former teammate Kevin Nolan will be able to help persuade Carroll to move south to London.
According to the paper, Liverpool will likely reject West Ham's offer as they look to reclaim at least £20 million for their record-breaking signing.