Councillors will take part in discussions next week, 19 October.
The purchase is one part of a wider flagship regeneration project for the area around the station which could unlock £50 million of investment in the borough.
The station gateway is the single biggest aspect of the Scarborough blueprint to transform the town centre.
A report, being presented to a meeting of the cabinet, will also ask for permission to buy the former Comet building on Westwood.
The Council's ambition is to radically improve the area around the railway station to create a more attractive entry into Scarborough for visitors and residents.
The road junction and public space would be remodelled as a 'station square' to make it easier to access the town centre from the station and to boost its visual appeal.
A new transport interchange would be created to provide more opportunities for people to travel around the area and leave their cars at home.
The proposals would include electric car hire and car clubs, a cycle and scooter hub, electric charging points and improved access to local bus and taxi services.
The 1970s concrete cladding on Pavilion House would be removed and replaced by glazing to give the building a modern look and to enhance its environmental credentials.
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The Council intends to create a public sector 'hub' in Pavilion House and we are in discussion with the NHS and Beyond Housing about their future accommodation needs.
The rest of the building would be offered as 'touchdown' workspace for businesses to use.
The proposal for the former Comet building is for it to be demolished and replaced with high-quality office accommodation.
It is earmarked for a new digital workspace called FabLab.
Fablab is a digital 'factory' which supports entrepreneurs to turn their ideas into products and prototypes by giving them access to advanced manufacturing technologies.
The scheme costs would be met by income from the sale of other council property and the already approved invest-to-save fund which was set aside to buy property in Scarborough.
It is also hoped a bid to the government's Levelling Up Fund will be successful, enabling a further contribution of funds towards the transformative work.
Councillors have previously agreed to a blueprint masterplan for Scarborough and a separate Town Investment Plan (TIP). It focuses on skills and enterprise, cultural activities, the environment, connectivity, well-being and sustainability.
Mike Greene, Chief Executive, said: "Our plans for the station gateway are bold, exciting and transformative.
"They represent the flagship element of our blueprint masterplan for Scarborough and would revolutionise how the area looks and feels.
"It has long been our ambition to deal with this ugly – and seemingly unloved – part of the town centre and I am delighted we are finally able to put our proposals before councillors.
"The creation of high-quality office accommodation and improved access to sustainable public transport will unlock huge economic potential for Scarborough and the borough."
David Kerfoot, chair of Scarborough Town Deal Board, said: "The proposals for the station gateway area of Scarborough are exciting and I am very much in favour of transforming this part of the town centre.
"First impressions are very important so when visitors to Scarborough currently arrive at the railway station they are greeted by a major road junction and ugly 1970s building.
"That's why the Town Bid feels we can we can do so much better and give those visitors an initial first class impression of the town.
"Further, the council's vision for high-quality office accommodation and a new transport interchange will create a much better proposition for business investment which is so important."
