Press Association Sport understands Liverpool flatly turned down the Magpies' loan bid but have made it known they would be willing to listen to offers for a permanent move.
New Reds boss Brendan Rodgers claimed last week that he would consider sending Carroll out on loan but, while the club were not commenting on the matter last night, it is understood a short-term move is now not on the agenda.
Instead Liverpool will attempt only to recoup some of the club-record £35million they paid to Newcastle 18 months ago should the right offer be tabled.
Whether the Magpies will now be willing to return with a new offer for the Gateshead-born striker, who has failed to live up to his hefty price tag since leaving the north-east, remains to be seen after their loan bid fell well short of anything the Reds might consider.
Liverpool have already strengthened in attack following the arrival of Rodgers following the signing of Roma striker Fabio Borini last week.
Rodgers' arrival has seemingly ushered Carroll towards the exit door with claims that the 6ft 3in striker does not fit in with the Northern Irishman's pass-and-move style of play.
That prompted West Ham to initiate contact over a possible loan move last week before Newcastle's bid, which contained an option for a permanent move, was tabled yesterday.
The Magpies have no immediate need to strengthen their hand in the striking department, although they spent the early part of the summer wooing FC Twente's Luuk de Jong but found the asking price too rich.
However, the spectre of the release clause in Demba Ba's contract makes him vulnerable, at least until the end of this month, although boss Alan Pardew insisted last week that there had been no contact with any club over any of his key men.
But Ba and Papiss Cisse could be required by Senegal for the African Nations Cup, while Leon Best and Peter Lovenkrands have left the club, so reinforcements will be required at some point.
Carroll's departure for Liverpool sparked a furious reaction in the north-east when a man around whom it seemed likely the team would be assembled was allowed to leave.
Newcastle had little intention of selling him until the final few hours of the transfer window when the Reds made an offer they simply could not refuse.
The forward had barely half a season of top-flight football under his belt, but 11 goals to add to the 19 he had plundered in the npower Championship a season earlier had marked him out as an emerging talent.
Dalglish was convinced he could prosper on Merseyside, but it simply did not happen for him in his first year or so at his new club, and his price-tag was repeatedly thrown back in his face as Ba and Cisse, the men signed from the proceeds, prospered on the other side of the Pennines.
He belatedly made an impression at the end of last season and was one of few England players to emerge from Euro 2012 with any credit after scoring a superb headed goal against Sweden.