The striker has found goals hard to come by since his £35m move from the Magpies a year ago.
"I am worried about the people that invent them," said Dalglish. "You have absolutely no foundation whatsoever [for the stories].
"I don't need to justify what is in the paper. I have stood up - and always will stand up - for the players."
Carroll spent five years on Tyneside before his high-profile move to Anfield.