The council's planning and development committee wrote to developer Barratt David Wilson Homes to ask if they would consider a primary residency scheme which could allow local families the chance to buy property in the town.
Whitby borough Cllr Phil Trumper, who sits on that committee, told the Gazette: "It's important to get young people and young families on the housing ladder which was a suggestion I put forward, supported by Cllr Clive Pearson and unanimously passed.
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"That would make sure that they are primary residences and not second homes.
"Developments such as that should be for local people, but they are so out of reach of people's affordability."
Cllr Trumper spoke to the leader of Cornwall Council about St Ives, another tourism hotspot, where a landmark vote in favour of a Neighbourhood Plan means that new-build housing projects will only be given planning permission if they are reserved for people who live in St Ives and surrounding areas full-time.
"It's similar to Whitby - it's a beautiful town with old fishermen's cottages going for half a million pounds," he said.
"It's similar on Church Street - prices are just ridiculous.
"People are coming in, buying them up and renting them out.
"It has a knock-on effect as it's then difficult to find people to work here.
"People will work closer to where they are living - why would they come to Whitby [to work]?"
Cllr Trumper said it is hoped the primary residency scheme can be put forward for Whitby and the surrounding area.
"We need local people and local families to get homes."