The Midlands club were prepared to offer Darren Bent - a reported target for Kenny Dalglish - as part of the deal.
But the Anfield boss is adamant he won't allow Carroll to leave, despite his poor form.
The latest gossip and rumours from the newspapers and online:Manchester City are prepared to pay Barcelona £100million for forward LIONEL
The latest gossip and rumours from the newspapers and online:The Sun says Chelsea striker DIEGO COSTA will call a truce
Pep Guardiola conceded Manchester City's Premier League title bid could be over after the heaviest domestic league defeat of his
It feels right again said Gary Neville, after United secured a 2-1 victory over Middlesbrough with an 86th minute winner
Wayne Rooney has the chance to officially break Sir Bobby Charlton's Manchester United all-time scoring record on Sunday - but
Manchester United host arch-rivals Liverpool at Old Trafford on Sunday.