Carroll left St James’s’ Park for Liverpool in a £35m move in January 2011, and is on a season-long loan at Upton Park.
The Hammers have the chance to make the move permanent for a cut-price £17m in the summer.
But, according to The Sun, they will allow Carroll, 24, to return to Anfield, and turn their attentions instead to Southampton’s Ricky Lambert.
Carroll scored 31 goals in 80 appearances for the Magpies between 2006-2011, and Alan Pardew has often said he would welcome him back to Tyneside.
But ... do we need a 'target man'? They seem to be well out of fashion in world football at the moment.
In the Premiership, the top three goalscorers this campaign are hardly 6ft 5" battering rams ...
Luis Suarez 21 goals
Robin van Persie 19
Gareth Bale 16