It will be the fourth time phone boxes in the district have been under threat since 2008 and each time the authority has objected to the proposals by BT, which has said where it receives objections from the local authority, it won't remove the pay phone.
A full meeting of the authority next week will hear ten of the 11 phone boxes are in areas identified as having inadequate mobile phone coverage.
While a number of them are infrequently used, residents say the call boxes remain a vital link for both residents and visitors due to unreliable mobile signal.
Other objections include that the local defibrillator would be rendered useless without a phone service as they required the ability to call 999 to obtain the access code.
However, the objections show the phone boxes are not only valued in rural areas, with Colburn Town Council arguing there is an identified need there as its public phone has been used 228 times in the last 12 months.
The phone boxes on the council's shortlist to campaign for include Arkengarthdale, Buttersett, Carperby, Carlton, Colburn, Aysgarth, Grinton, Hudswell, Muker, Preston under Scar, Reeth and Newsham.
In addition, communities at Redmire, near Leyburn and Gayles, near Richmond, have expressed an interest in 'adopting' their red phone boxes - which were designed in 1935 to commemorate the silver jubilee of King George V - at a cost of £1.
The Yorkshire Dales National Park Authority has confirmed it wishes to see all payphones within the park retained unless it can be clearly demonstrated that there would be no significant detrimental effect upon local communities and visitors.
A national park authority spokesman said it does not consider that, through the application of BT's generic criteria, adequate consideration has been given to the specific circumstances of a deeply rural area like the national park.
In 1992, before mobile phones became popular, there were 92,000 phone boxes across the UK. BT says many phone boxes have become expensive to maintain.
The cost to BT of maintaining the phone boxes annually is about £6m.
BT is responsible for repairing damage to the kiosks, including replacing glass panes and broken receivers, as well as removing graffiti, rubbish and human waste, which it regards as a burden on the firm.
A spokesman for the firm said it would consider the views of residents before making a final decision on the future of the phone boxes, the use of which has declined by more than 90 per cent in the last decade.
The firm says the need to provide pay phones for use in emergency situations is diminishing all the time, with at least 98 per cent of the UK having either 3G or 4G coverage.
The spokesman added: "This is important because as long as there is network coverage, it's now possible to call the emergency services, even when there is no credit or no coverage from your own mobile provider."