The Welsh Government said it wants to understand what its focus should be for improvements.
But whether restructuring of Betsi Cadwaladr health board features would depend on what the public says.
A government spokesman disputed Welsh Tory criticism over whether a deadline to start the exercise had been missed.
The health board, which serves north Wales, was put into special measures in 2015 after a report found "institutional abuse" at a mental health unit.
A spokesman for the Welsh Government said: "One of the key objectives is to engage with staff, patients and communities to understand what matters most to them and what the focus should be to deliver improved outcomes in health services.
"The first phase involves discussions with partners and regional stakeholders and this work commenced in August. The second phase will take place in the autumn and will involve digital and community engagement with the public."
He said it would "depend on the views and responses provided if restructuring features".
First Minister Carwyn Jones had hinted the health board could be broken up after the 2016 assembly election.
But the Welsh Labour assembly manifesto vowed "no top-down, large-scale reorganisation" of the NHS under the next Welsh Labour Government - the same document said it would review the board's "governance structure if necessary".
Welsh Labour promised in its manifesto before May's assembly poll that it would hold "discussions with people in north Wales about the future of Betsi Cadwaladr University Health Board" in "the first 100 days of the new assembly term".
Aberconwy Tory AM, Janet Finch-Saunders, said it was "a deadline the Welsh Labour Government really ought to have met".
"One would have hoped that engaging with the public would have been an immediate priority for the government which led the health board into special measures in the first place," she said.
A Welsh Government spokesman said in response: "These comments undermine the positive progress made by the board in delivering improvements since they were put in special measures."
He said: "Contrary to comments from the Conservatives, that process has already begun and a second phase will take place in the autumn that will involve engagement with the public as we want to know what, in their health service, matters to them the most."

The midfielders have both agreed three-year deals at Dens Park.
Williams, 28, moved to the Highlands in the summer of 2013 from Kendal Town and has made 35 appearances this term.
Former Kidderminster player Vincent, 26, also joined in 2013 and scored the winning goal when Caley Thistle won the Scottish Cup last season.
Vincent has been troubled by injuries this season and has been limited to 16 outings, the last of which came on 2 January.
"It's two boys we've been chasing for a long time," manager Paul Hartley told BBC Scotland.
"They've been part of a very successful Inverness team over the last couple of seasons.
"Danny is versatile, he can play in a number of positions. It's the same with Vincent, anywhere across the middle."
Meanwhile, Paul McGowan and Darren O'Dea have signed new contracts at Dens Park.
Midfielder McGowan, 28, has agreed a two-year extension, while former Celtic defender O'Dea, 29, has earned a three-year deal, having joined the club in January.
"We've been trying to build a squad over the last two years and this summer there will only be maybe three or four changes," added Hartley.
Members of the public in north Wales are to be asked their views on the future of their region's health service this autumn.
[NEXT_CONCEPT]
Inverness Caledonian Thistle duo James Vincent and Danny Williams have signed pre-contracts to join Premiership rivals Dundee next season.