The leader of Devon County Council is "extremely hopeful" the authority can freeze council tax this year.
John Hart, Conservative leader of the council, signalled the average home in Devon would continue to pay the authority a £1,116 annual charge from April.
The controlling Conservative group is expected to meet shortly to draw up proposals for the levy in 2013-14.
Ahead of the meeting, Mr Hart said: "I am extremely hopeful we can freeze council tax for the third year running."
If agreed, the move would be in contrast to neighbouring Cornwall Council, a Tory-led coalition, which is proposing a bills hike of 1.97% this year, a £25 rise to about £1,268.
The authorities would be taking a starkly different approach to an offer from Local Government Secretary Eric Pickles. For the third year in a row, his Whitehall department has promised to give councils a cash bonus to the equivalent of a 1% increase in council tax if they hold down the charge.
But to add to the dilemma, councils that raise the levy by 2% or higher will have to hold a local referendum to get consent for the change.
Cornwall's Tory council leader Jim Currie has said increasing the tax is the "only option" to protect frontline services.
A Government minister this week accused Cornwall Council of "democracy-dodging" after proposing a hike in council tax that falls just short of the threshold.
Whatever the two authorities decide, both go to the polls in May during a round of local elections across the country.
Devon County Council is likely to argue it started to make savings before the latest round of cuts to central government hand-outs. But Devon taxpayers are still likely to face small increases to their bills from district councils – unlike Cornwall which has a single "unitary" authority.
Yesterday, Exeter City Council announced it is proposing to put up its council tax by 4%. It means occupiers of an average Band D property face paying an extra £5 a year from April.
Council leader Pete Edwards said: "Government funding to Exeter has been severely cut again. We must increase council tax to protect essential services."
Mr Pickles has permitted small district councils to raise council tax by up to 4% without a referendum. In the Westcountry, the councils with council tax low enough are East Devon, South Hams, West Dorset, Taunton Deane, Sedgemoor and West Somerset.