Brendan Rodgers expects a quick resolution to Andy Carroll's future at Liverpool, with the striker's hopes of a return to Newcastle United receding.

West Ham United have had a £15m offer accepted by Liverpool for the 24-year-old, who was initially reluctant to move to east London on loan last season and who harbours similar doubts over signing for Sam Allardyce's team on a permanent basis.

The England international has not given up hope of revitalising his career at Anfield, despite being told by the Liverpool manager that he will have few opportunities to do so, but he would consider a move back to the boyhood club he left for £35m in January 2011. Newcastle, however, have not registered an interest and a potential exchange deal involving Hatem Ben Arfa is unlikely as Rodgers' interest in the French midfielder has cooled.

Rodgers said: "It was just a general conversation in terms of the experience of getting out and playing. He enjoyed that apart from the injury. At the start of the season the whole thing was about going and getting games because he wasn't going to be a starter here. We will talk again with him and the club to see how it all evolves. It's one of those situations where it will probably be resolved a lot quicker than that for both parties."

Liverpool were keen on Ben Arfa earlier in the season and a swap for Carroll may have appealed to Newcastle, who refused to entertain the striker's £17m asking price last summer and attempted to re-sign him on loan instead. But Liverpool were unimpressed by the 26-year-old France international following his return from a three-month injury lay-off in March and that avenue now appears closed to Carroll.

Carroll scored seven goals in 24 league games for West Ham to earn a recall to the England squad for the friendlies against the Republic of Ireland and Brazil, a recall since postponed by a heel injury. As was the case last summer, Carroll has been told he does not feature in the Liverpool manager's long-term plans and Rodgers wants to invest the £15m fee and a salary in excess of £4m in new faces. Schalke's Greece international Kyriakos Papadopoulous is his main target to replace Jamie Carragher in central defence next season and Liverpool may have to pay more than £12m for a player targeted by several leading clubs. The Anfield club are also leading the chase for Barcelona's 16-year-old winger, Sergi Canos, who is also wanted by Arsenal and Manchester City.

On his end-of-season talks with Carroll, the Liverpool manager said: "It's a difficult one. I spoke to him and we had a good chat. The boy is a talent. It's just something we need to assess between now and the end of window. In terms of the money, that's something out of my control. But he's a talent so we will assess the whole situation. The objective at the beginning of the season was for him to go out and play. He's gone away to think of what we spoke about and we will talk again through the weeks."

In contrast to last summer, however, when Carroll joined West Ham shortly before the transfer deadline and Rodgers was unable to sign Clint Dempsey as a replacement, Liverpool want to resolve the striker's position quickly.