Reports suggested the £35million club record signing's former club Newcastle were preparing a cheeky cut-price bid to take the England international back to his native North-East.
The Magpies have played down the speculation and it's believed there has been no contact between the two clubs.
Caroll's representatives have also insisted they have neither been told to look for, nor are seeking, a move for their player.
Dalglish was dismissive when asked about whether the rumours could unsettle the striker, who has scored four goals this season but has yet to find his best form since his transfer to Merseyside almost 12 months ago.
"I am worried about the people that invent them," he said.
"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."
Turning the argument around on journalists at his post-match press conference after the 1-0 Carling Cup semi-final first leg win over Manchester City Dalglish added: "You justify your profession and you justify the story."