The towns are the only major places in North Yorkshire not to be parished and could be given control over areas including parks, tourism and events when the county and borough councils are abolished next April.
Councillor Carl Les, leader of North Yorkshire County Council, said he has faced calls from local politicians, businesses and community groups for the town councils to be created.
But he added it would be up to residents to decide via a vote whether the plans should go ahead.
"That said, it is for the people to decide whether they want them or not.
"I'm very keen that we start the process as soon as possible and we will go to the public in Harrogate and Scarborough at the earliest opportunity."
The creation of town councils would require a community governance review and it is understood that legal powers to start the process have been handed to the county council's new executive.
Councillor Les said the legislation was now being examined and that the authority would work alongside Harrogate and Scarborough's borough councils.
He also said it would be "logical" for the town councils to be created after the new North Yorkshire Council launches next April.
His comments come after councillor Pat Marsh, leader of Harrogate's Liberal Democrats, made calls for the process to start "within the next couple of months."
When asked when the referendums could be held, councillor Les said this was currently unclear but he added it would be "as soon as possible".
He said: "We are getting a lot of requests about town councils made to us from people including local politicians, as well as the business community and groups like Harrogate Civic Society.
"There is clearly an appetite to do something about this.
"And of course the sooner we can do it, the sooner we can find out whether there is an appetite amongst the general population.
"They are the key people in all of this. They have to be asked for their opinion and will say yea or nay."
Councillor Les also said there was a possibility that more than two town or parish councils could be created - if that's what voters wanted.
He said: "Another aspect to this of course is - how many councils?
"Would Harrogate or Scarborough just want one town council each, or perhaps there are options to consider about the various parts of the towns being parished.
"This is all part of the work that will have to be done."
By Jacob Webster, Local Democracy Reporter