The lawyer for Dr. Eilish Cleary, Robert Basque, says he is in negotiations with the province over the abrupt dismissal of his client.
"I'm talking to the government lawyers about sorting things out," said the Moncton-based lawyer.
Tom Maston, deputy minister of health, said in a statement released late Thursday afternoon, "Government lawyers have received an offer to settle from Dr. Cleary's lawyer today, which they are currently reviewing."
New Brunswick's recently fired chief medical officer of health cancelled a scheduled appearance on Information Morning Fredericton on the advice of her lawyer.
Dr. Eilish Cleary was planning to be a guest on the radio program Thursday morning, but cancelled Wednesday evening.
"I was asked by government lawyers not to speak publicly and my lawyer advised we accommodate their request," said Cleary in an emailed statement to CBC News.
In his statement, Maston said Cleary's statement was inaccurate. Maston said it's a breach under the New Brunswick Law Society's professional code of conduct for a lawyer to directly contact the client of another lawyer.
"Dr. Cleary's statement today implies that government lawyers committed such a breach. This is not the case, as confirmed by Dr. Cleary's lawyer.
"There was an agreement of all parties that they would not talk publicly while negotiations were ongoing. Unfortunately, government was refused its request for consent by Dr. Cleary to discuss the details of this matter. Without consent, government is unable to respond to comments made by Dr. Cleary and others. As this is a personnel matter, we believe it is appropriate not to comment to protect the privacy of the several parties involved."
Basque told CBC News the government's lawyer suggested to Basque that it would be easier to sort things out if Cleary were "to stay out of the press."
Cleary was hired as the province's chief medical officer of health in 2008.
She said she was told she was being placed on leave on Nov. 2.
On Dec. 7, government lawyers told her lawyer she was being terminated.
The Department of Health will only say Cleary's firing is not politically motivated or related to her medical and scientific work.
Cleary's only public statement since the firing has been to state that she was fired "without cause" and is "considering next steps."
A number of advocacy groups have rallied to Cleary's defence and launched a campaign to have her reinstated.
In 2012, Cleary put together an 82-page report looking at social and community health risks in New Brunswick if a shale gas industry is to be developed in the province.
At the time she was placed on leave, Cleary was studying the use of the herbicide glyphosate in New Brunswick.