The News of the World reported that the pair were critical of some of manager Gerard Houllier's coaching staff during a team break at a Spa in Leicestershire.
"I apologise unreservedly for my behaviour on Wednesday night. It was not acceptable and I am genuinely sorry," Dunne told the newspaper.
Collins added: "We were wrong. This should not have happened and I apologise for the part I played."
The club are now due to launch a review of the incident, with a spokesman adding: "We have launched an investigation in line with our internal disciplinary procedures."