Andy Carroll was supposed to be relaxing at a plush Brazilian resort and yet, even as he soaks up the sun and attempts to let those flowing locks down, he must now feel frazzled again. It is only a month since the forward was leaping to meet Steven Gerrard's delivery and thunder a glorious header beyond Andreas Isaksson, an England goal crafted in Liverpool to rouse a vocal minority within Kiev's Olympic Stadium. Back then it appeared a watershed, the moment a player proved he belonged. Now it feels more like a false dawn.

Carroll will wonder at this depressing reversion to type. He had travelled to Euro 2012 propelled by a late-season flurry of form with Kenny Dalglish's Liverpool and with his mood presumably improved further when Brendan Rodgers' appointment back on Merseyside suggested the club was embracing reinvigoration. And yet, even before he has benefited from a training session under the new regime, the 23-year-old is now painfully aware that his days at Anfield are numbered.

A striker who would not appear a natural fit in the style and system Rodgers intends to implement has effectively been rendered available for transfer. There were times last term when he must have felt superfluous, his rhythm lost in an inability to string together a prolonged run of Premier League starts. Even before the new term is underway, life on the periphery merely feels maintained.

The reality as to whether he stays or goes before the new season has descended already into a game or brinkmanship between Liverpool's hierarchy and a string of suitors led by his former employers, Newcastle United. Those at Anfield will only countenance a sale worth £20m. Newcastle, Aston Villa and West Ham would prefer a loan move, possibly with a view to a long-term deal, though their valuations will not match Liverpool's for a player who was bought on impulse and has since mustered 11 goals in 56 games in his 18 months at the club.

This has the makings of one of those all too familiar sagas – they seem more usually to feature Arsenal – that resolves itself only when panic sets in and the transfer deadline is upon us at the end of August. Unless, of course, Carroll ends up being granted an opportunity to impress upon linking up with Liverpool's squad in the United States next week and goes on to persuade the management that he should have a future at the club.

Instinctively compromise feels unlikely. There has already been at least one telephone call between Rodgers and Carroll, during which the player was apparently told "exactly where he stands". On the face of it theirs does feel like an awkward relationship. Much is made of the precise passing routines and possession play demanded by Rodgers at Swansea, which will form the basis of Liverpool's approach next season, and that technique-based system would hardly appear suited to tapping into Carroll's strengths as a line-leader and old school English centre-forward.

Just as integral to the adopted pattern of play will be the pressing required to regain the ball when it is surrendered. While he is imposing in the air and possesses a hammer of a shot, the 6ft 3in forward is not the most mobile on the turf. Rather he has other assets – England have benefited at times from his hold-up play when they have gone more direct, and his impact as a battering presence for his club in scraps against Everton, Blackburn Rovers and Chelsea last season was obvious – but, if the frontline cannot harry and hassle, then gaps will appear behind and the collective suddenly feels lightweight.

Rodgers had spoken of loaning the forward out, suggesting games elsewhere for players on the fringes "can benefit the club in the long term", though it seems unlikely that Carroll would ever return better placed to fit into the manager's favoured approach. The only surprise in his apparent willingness to discard the striker is the lack of an obvious Plan B.

Liverpool are anxious for their new head coach to thrive and concede he will need time to make a proper impact but they will also demand positive results through the inevitable period of adjustment to come. If they are chasing matches while Rodgers is still implementing his preferred style, would the option of casting Carroll into the fray as a battering-ram impact player not be beneficial? The manager seems unconcerned by the issue but others might suggest a player who had just started to show his true capabilities last spring might remain an asset worth utilising.

Carroll, it seems, is resigned to leaving. Where once he was bullish and bolstered by his effective cameos with the national team, now he would apparently favour the thrashing out of a move back home to Tyneside. He understandably needs to feel wanted and there is an irony that, at the time of writing, he would seem far more likely to start England's friendly against Italy in Berne on 15 August than Liverpool's opening Premier League fixture at West Bromwich Albion three days later.

That feels unsatisfactory and, if he has not played consistently and remains a Liverpool player as the transfer deadline passes, his involvement with Roy Hodgson's team in the World Cup qualifiers against Moldova and Ukraine in September would surely be forfeit. Similarly life on the fringes at Anfield will merely prolong the circus, the questions forever revolving around whether he is to be included from the start against Arsenal, Sunderland or Norwich, or even in an unappealing Capital One Cup tie or Europa League fixture. That will become tiresome, as much for the questioners as the club and their player.

A compromise may have to be reached eventually to sanction another fresh start. Upon signing Carroll in January 2010, John W Henry had shrugged off fears over the size of the £35m fee by stressing that the key had always been Liverpool's ability to prise £15m more from Chelsea to secure Fernando Torres. "Those prices could have been £35m [from Chelsea for Torres] and £20m [to Newcastle for Carroll], 40 and 25 or 50 and 35," he said. "It was ultimately up to Newcastle how much this was all going to cost. They [Newcastle] made a hell of a deal. We felt the same way." At some stage Liverpool will have to accept that blinding deal has now been exposed as a loss. Disappointing as it may be for Carroll to accept, particularly with memories of Kiev still smouldering, a parting of the ways might be best for all.