Carroll himself made a statement on Monday morning insisting he was staying at Liverpool and his manager Kenny Dalglish has now reinforced that and refused to comment on whether the swap deal rumour is true.
"We don't have any problem with any of our players because nobody is going anywhere," he said. "Just read what Andy said this morning. He said he's very happy here. He doesn't regret coming here. That's the best reference you can get.
"We don't need to comment. We've said what's going to happen and it's nothing, so that's us. We don't need to get involved to justify what people have said. Ask them to justify it, not us.
"I am not talking about any specific incident but if you are going to do business in any way, shape or form in whatever life it's in, you don't disclose it until it's done, do you?
"As we've said before, and [the chairman] Tom Werner said, there's no point letting the facts interfere with a good story. They said we bought Stewart Downing off YouTube. Do me a favour."