Press Association Sport understands the Magpies will look elsewhere as they attempt to bolster a strike-force which was severely depleted by Demba Ba's January departure for Chelsea.
Manager Alan Pardew has repeatedly spoken of his willingness to consider bringing the now 24-year-old England international, who was sold to the Reds for £35million in January 2011, back to St James' Park.
But the club failed in a cheeky attempt to sign him on loan last summer after it became clear he had little part to plan in Brendan Rodgers' plans at Anfield, and he headed for West Ham instead.
The Hammers have made little secret of their hopes of securing the services of the Gateshead-born frontman on a permanent basis and have agreed a fee of £15million plus add-ons, with the decision now in Carroll's hands.
With Newcastle having let it be known they will not compete for his signature, West Ham's position looks to have been strengthened.
Pardew was due to meet owner Mike Ashley and managing director Derek Llambias on Wednesday to thrash out the way forward after a desperately disappointing season, which saw the Magpies come within touching distance of the Europa League semi-finals, but also flirt alarmingly with relegation from the Barclays Premier League.
They sold Carroll barely a month after Pardew's arrival on Tyneside after Liverpool made them an offer they simply could not refuse, but the striker struggled to make an impact on Merseyside and Kenny Dalglish's untimely exit heralded a further downturn in his fortunes.
Pardew had no desire to let the player leave - indeed, he had repeatedly insisted he would be going nowhere until the Reds broke the bank to get their man - and whenever asked about a possible return, he has always indicated his willingness to see the 6'3" powerhouse back in a black and white shirt.
When it became obvious that his short-term future lay away from Anfield, Carroll was keen to return to familiar territory, but it was West Ham who eventually managed to reach agreement, with the Reds simply unwilling to deal with the club which had profited so substantially from their initial investment.
But interestingly, Pardew was more coy just last week when asked about Carroll.
He said: "He's a player that anybody in the Premier League has got to be interested in if he becomes available."
The money Newcastle received for Carroll was used to secure the long-term futures of Tim Krul, Fabricio Coloccini and Cheick Tiote as well as to sign the likes of Yohan Cabaye, Papiss Cisse and Ba, and it was Pardew's belief that they had moved on.
However, Ba's exit has left them painfully short and Cisse struggled in a lone-striking role during the second half of the campaign.
Newcastle have invested much time in attempting to add firepower after chasing the likes of Luuk de Jong and Loic Remy without success, and that search will continue this summer.
Carroll now appears to be off their wish-list, although it remains to be seen whether that position is maintained or is simply a bargaining ploy or a tacit admission that the Hammers have won the race to sign him.