The unwanted Anfield flop is top of the list of priorities for Hammers boss Sam Allardyce, who has already agreed a loan deal for the striker worth £2m with a further £17m should the east London team maintain Premier league status this season.
“West Ham are not giving up on this,” an Uptown Park source has told The Sun newspaper.
“The manager wants him badly and the board are backing him to the hilt.”
Carroll was the subject of an audacious transfer day move from Newcastle to Liverpool in January 2011 for a sum of £35m, a record for British player moving between British clubs at the time. He failed to make an impression for the Reds, though, scoring just six goals in 42 appearances.