The English striker, who made his move to West Ham permanent in June last year, says he told his new team-mates during pre-season that Brendan Rodgers' men would threaten.
Sitting two points clear at the top, Liverpool – who face West Ham on Sunday – are dreaming of a first league title since 1990.
And Carroll said he predicted the Anfield club to challenge with star strikers Luis Suarez and Daniel Sturridge starring.
"I said from the beginning of the season that I thought they had a great chance of winning the league," Carroll said.
"I said that from the beginning – the very start. I said to all the lads that they would win it.
"All of them were ifing and butting, but I turned around and said it. They will back me up. From the beginning. I just had a feeling.
"They signed Sturridge who's a great player as well, and having played with Suarez and knowing what he's like, having those two together, the way they connect together, they are unbelievable. They look unbeatable."
Carroll failed to live up to his £35 million price tag at Liverpool during 2011-12 and made a permanent move to Upton Park after a loan spell at West Ham.
But the 25-year-old insists he has no regrets, pointing out the 'incredible' form of Suarez and Sturridge who have scored 49 league goals between them.
"The way they are playing, they have the players to do that: Suarez and Sturridge up front are completely different to me. The way they play is incredible," Carroll said.
"No bitterness at all, no. I moved to West Ham and I am loving it - apart from the injury set-back everything has been great."
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