Liverpool accepted a bid from the Hammers which would have seen Carroll go on a season-long loan to Upton Park for £2million, leading to a further £15million and a permanent move providing Sam Alardyce’s side avoided relegation.
But Carroll has turned down the opportunity to join the Premier League newcomers, and instead stay at Anfield to fight for his place up front.
New Reds boss Brendan Rodgers could still yet include Carroll in his plans for the new season, with other striking power coming from Luis Suarez and Fabio Borini.
Craig Bellamy is also competing for an attacking starting place with Rodgers’ style of football thought to favour a three-man strike force.
Carroll has also been linked with a return to boyhood club Newcastle Utd this summer, but the Magpies are unwilling to match Liverpool‘s asking price and Rodgers is thought not to be keen on selling to a league rival.