The Reds boss was delighted after his side's 1-0 win over Manchester City in the first leg of the League Cup semi-final, but quashed rumours linking the striker with a move away
Reports on Wednesday linked Carroll with a shock return to Tyneside this month but Dalglish issued a firm denial when asked if he was worried about losing the striker.
“I’m worried about the people that invent them,” Dalglish said after his side’s win over Manchester City in the first leg of the League Cup semi-final on Wednesday night.
“It has absolutely no foundation whatsoever. I don’t need to justify what’s in the paper. That’s your [journalists] job. I have not heard any Andy Carroll rumours.”
Carroll was part of a side that won 1-0 at the Etihad Stadium thanks to a penalty from captain Steven Gerrard in the 13th minute.
It leaves the Reds in pole position to reach the League Cup final ahead of the second leg at Anfield on January 25.
Dalglish hailed a “fantastic” Liverpool performance but warned his side will have to be at their best as the Merseyside club go in search of their first trophy since 2006.
He added: “We might have a slight advantage with the goal but there’s no-one jumping through hoops at our place.
“It's not finished unless they want to withdraw. I don't think they're going to do that! We have to stay professional.
“It was two different performances in each half. The first half we were more threatening, but in the second half we battened down the hatches.
“Not too many teams have come here and got no goals against them. It might not have been the prettiest of performances but we needed desire and ambition.
“Once we were in front we were determined not to lose. It was a fantastic performance by the players against a good side.”
Dalglish also eased fears over the hamstring injury that forced off midfielder Jay Spearing in the 23rd minute while he reserved special praise for matchwinner Gerrard.
“Jay Spearing has not pulled [his hamstring] in any way, shape or form I don't think. It's just a bit tight,” he said.
“Steven is going to get better every time he plays a match. It’s great to see him back. He has a great influence on everyone.”
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