McNeil said a letter from the provincial Justice Department had been sent Tuesday to lawyers representing the 150 former residents of the Nova Scotia Home for Colored Children.
"I have made it very clear coming into the election there would be a very different tone taken in terms of this file," said McNeil, whose Liberal government was elected Oct. 8.
McNeil wouldn't say what a potential dollar figure could look like but said a settlement would only be reached if both sides are able to agree.
"There's obviously a financial implication here we know that, but there is also the right thing to do," he said.
McNeil said if an agreement can't be reached then it would be left to the court to decide.
He also said the outcome of any negotiation wouldn't affect his campaign promise to hold a full public inquiry into alleged sexual, physical and psychological abuse at the facility over a 50-year period up until the 1980s.
McNeil has previously said the inquiry could take place as early as next spring.
The attempt to settle out of court is a departure from the path taken by the previous NDP government, which challenged affidavits submitted to the court.
The allegations in the class-action have not been tested in court and previously lawyers for the government have argued that some of them are based on speculation or hearsay.
Tony Smith, who is part of the class-action and is spokesman for the Victims of Child Exploitation Society, welcomed the Liberal government's initiative.
"I think it's quite encouraging news . . . it gives an opportunity to look at addressing the healing process a lot sooner than later," said Smith.
He said a satisfactory settlement would be more preferable than continuing with what would likely be a lengthy court process.
In April, the Home for Colored Children agreed to pay a $5-million settlement to 140 plaintiffs after a class-action lawsuit was launched two years ago.
A Nova Scotia Supreme Court judge is yet to rule on whether to certify the current class-action.