The plans could be referred to ministers by the local patient watchdogs, the community health councils (CHCs).
BBC: Betsi Cadwaladr and Conwy council in health shake-up talks
The government would look at proposals in detail if they are referred by CHCs, Mr Jones said.
CHCs have six weeks to refer the plans or any part of the plans to Health Minister Lesley Griffiths.
The association has fought a long campaign against plans to scrap CHCs, and has won support from many quarters.
Decisions about whether to approve the changes could be referred to Mrs Griffiths if Community Health Councils (CHCs) object.
BBC: Wales NHS change: CHCs want strong political leadership
Local CHCs are the only bodies with the legal right to refer proposed NHS changes to Health Minister Lesley Griffiths.
Mr Jones told the Sunday Politics programme the government would look at proposals in detail if they are referred by CHCs.
BBC: Betsi Cadwaladr and Conwy council in health shake-up talks
It also argues that the lack of overlap between CHCs and their replacements will leave the public without adequate representation for months.
Opposition parties have previously criticised Mrs Griffiths for her attitude towards CHCs.
BBC: Wales NHS change: CHCs want strong political leadership
CHCs are proven to reduce ethnic and racial disparities in care.
WHITEHOUSE: New Recovery Act Funding for Community Health Centers
He said that the minister's proposal to cut the number and membership of community health councils will seriously inhibit the ability of CHCs to adequately represent patients.
He told BBC Wales' Sunday Politics programme that changes to the NHS in Wales were necessary but the government would look at proposals in detail if they are referred by CHCs.
Paul Worthington, from the Board of Community Health Councils in Wales, the national body that represents CHCs, told BBC Wales' Sunday Politics programme that politicians will have to look at the bigger picture.
BBC: Wales NHS change: CHCs want strong political leadership
Ms Davies added that she would be letting the Welsh health minister know that the CHCs needed additional funding if they were to produce every single one of its documents in a bilingual format.
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