The 25-year-old's former club are two points clear at the top of the table with six more rounds of matches left this campaign.
"You know, I said from the beginning of the season that I thought they had a great chance of winning the league," The Mirror quotes the England international as saying.
"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 [Daniel] Sturridge who's a great player as well, and having played with [Luis] Suarez and knowing what's he like, having those two together, the way they connect together, they are unbelievable. They look unbeatable."
Carroll was on the books of Liverpool between 2011 and 2013.