West Ham had a £15 million bid accepted by the Reds last week.
The Daily Star says the hitman has told friends he is on the verge of signing a six-year deal.
Carroll was hoping for a pay rise to £100,000 a week to join the Hammers permanently, after his season-long loan spell last term.
West Ham matched Carroll's £80,000-a-week Liverpool wages last season but were reluctant to stump up another £20,000.
But his revelation suggests a compromise is close to being reached.