Liverpool have accepted a £15m offer from West Ham United for Andy Carroll, a £20m loss on their record signing in 28 months, but face a struggle to convince the striker to sever his Anfield ties for Upton Park.

Carroll enjoyed an impressive yet injury-hit season on loan with Sam Allardyce's team, who have moved quickly to secure the 24-year-old on a long-term basis following their final Premier League game. West Ham are prepared to pay a club-record transfer fee to sign the striker around whom Allardyce intends to build his team, while Liverpool want to sell Carroll to generate extra transfer funds for the manager Brendan Rodgers.

In an eventful day for Carroll, he withdrew last night from the England squad to play the Republic of Ireland and Brazil due to a heel injury. The FA said it would not be calling up a replacement for the striker, who has not been involved with the national team since October's World Cup qualifier in Poland, when he was an unused substitute.

Rodgers, who admits he is braced for bids for Luis Suárez this summer, has lined up Kolo Touré on a free transfer from Manchester City and has made a £12m offer for the Schalke central defender Kyriakos Papadopoulos.

Liverpool wanted a £17m fee written into Carroll's loan deal when he reluctantly moved to east London last August. That was dropped to enable the move to proceed ahead of the transfer deadline, with West Ham paying a £2m loan arrangement fee and the striker's £80,000-a-week wages.

The agreed deal is a huge reduction on the £35m Newcastle United received from Liverpool in January 2011 but underlines the Anfield club's determination to offload Carroll and reinvest quickly.

Rodgers told the striker upon his arrival as Liverpool manager last summer that his first-team chances would be severely restricted and that stance has not altered. Carroll, however, is not sold on the idea of a transfer to West Ham, despite tweeting after the final game against Reading on Sunday that he had "enjoyed every minute" of his time with the club.

Rodgers and Allardyce have to persuade the striker that West Ham is in his best interests again, as they did last summer, but Carroll has so far given no indication he wants to leave Liverpool. He has taken encouragement from how Jordan Henderson and Stewart Downing revived their Anfield careers having been dismissed as expensive mistakes.

Carroll believes he can follow suit and would also consider a return to Newcastle United but West Ham, who are to part company with Carlton Cole, are the only club to submit an offer so far.

Rodgers is ready to sell Carroll despite the uncertainty surrounding Suárez's future at Anfield. The Liverpool manager was unable to provide assurances that the Uruguay international would stay in the aftermath of his 10-match ban for biting Branislav Ivanovic last month, when a despairing Suárez was considering his future in English football.

Rodgers has been encouraged by the player's demeanour since his return from a short holiday but accepts offers for Liverpool's leading goalscorer are inevitable this summer. "I don't have any doubts about that because he's up there," the Anfield manager admitted.

"There's a small percentage of players who are world-class and he's in that bracket so I don't think it will be too dissimilar to when I first came in last summer. People will want to take him. But he was committed to wanting to stay and work with the club. I think he's very happy here.

"Obviously he had a circumstance which made it extremely difficult for him but I've seen nothing to make me think otherwise. I've been in contact with his agent and I think he needs to go away, play in the Confederations Cup, have a period of reflection and come back raring to go to help us have a good season."

Rodgers believes Suárez's disillusionment with English football has lessened in the four weeks since his ban. "There was that initial period of shock and anger but a wee bit of reality has set in now," he said. "He knows he did wrong. Apart from those first few days when I gave him a period away, he's come back and he's got on with it."

The Liverpool manager also hopes the club's firm support for Suárez during another controversy will be repaid by the striker this summer. Rodgers added: "We as a club and I as a manager have supported him, told him when he's been right and when he's been wrong. The supporters show their passion for him relentlessly so as a club I don't think we can do any more.

"We have supported him when he's been in turmoil and when he's had setbacks, when there's been traumas over the last couple of years. As a club we're doing everything to keep him and all the players content, and in the main I think they are."