Healthscope's proposal comes amid financial restructuring and moves to outlaw similar partnership models in Australia's largest health system.
The operator and the NSW government say they are both focused on ensuring continuity of patient care at the 488-bed hospital as negotiations take place.
Two-year-old Joe Massa died after he and his parents spent three hours waiting in the emergency department at Sydney's Northern Beaches Hospital in September.
His mother Elouise Massa welcomed news of the proposal on Thursday.
"If this offer means an end to public-private partnership at Northern Beaches Hospital then it can only be a good thing," she said in a statement.
"Public-private partnerships in healthcare should never have been allowed to happen."
Premier Chris Minns in March announced moves to outlaw any future partnerships, which would not apply retroactively.
But Healthscope chief executive Tino La Spina told AAP the announcement had sent a clear message about the partnerships.
"Continuing to operate one seems to be inconsistent with those objectives and all we're saying is we're happy to work with the government to hand (the hospital) back if that's what they want to do," he said.
The proposal comes amid financial troubles facing the Canadian-controlled firm, but Mr La Spina said it had nothing to do with the company's financial restructuring.
Treasurer Daniel Mookhey told reporters the proposal will be subject to strict scrutiny.
"We do not want to see the private equity owners make a windfall gain at the public's expense as part of a going-out-of-business sale," he said.
He acknowledged some taxpayer money could be handed over as part of the commercial negotiation of the hospital's return.
But it was wrong to suggest the government's plans to outlaw future partnerships had prompted the proposal, Mr Mookhey said.
"We are paying attention to the wider commercial dynamics that are happening right now when it comes to this distressed business," he said.
"We do not expect any operational disruption whilst these conversations are taking place.
"Insofar as Healthscope's capacity to continue as a going concern, we are obviously preparing for all contingencies."
Mr La Spina similarly said continuity of care will be a key focus amid negotiations.
It could take up to a year to transition the hospital back into public hands, he said.
Healthscope, which operates 38 hospitals across the country, was due to operate the hospital until 2038, after it replaced two smaller public facilities in 2018.
The proposal comes amid an inquiry into the safety and quality of the hospital's health services.
A review into Joe Massa's death found an IT system not used in government-operated public hospitals had failed to alert nurses and doctors to the boy's concerning heart rate.
Joe's death was a truly tragic event which deserved proper scrutiny, Mr La Spina said.
"But we also need to ensure that we have a fair assessment of what the hospital's doing, and this is a great hospital, I stand by that," he said.
