It will have six bedrooms - four with balconies - three bathrooms, three living areas, a wine cellar and separate offices for the couple.
Outside will be a built-in barbecue, swimming pool and spa with bathroom, and automated gates at the entrance.
The existing concrete tennis court, now used as a carparking area, will be resurfaced with synthetic turf. A four-car garage will have a loft on top.
Mrs Hussona told the Herald she and her husband paid "a lot more than we wanted to" because they were pushed up at auction by two developers who planned to build a handful of houses on the site.
She said neighbours were keen to see the hostel go because it was noisy, attracted a lot of traffic and produced a lot of rubbish.
A heritage architect had described the old building as being in "complete disrepair" because it had been renovated so many times.
She said the site was unique as large sections did not come up for sale often in Mt Eden and it had views of the Waitakeres and the Sky Tower.
The Auckland Council is considering Mr Hussona's resource consent application, which is open to public submissions.
The present owners bought the property for $450,000.
The hostel's lease ends in September.
22 Pentland Ave, Mt Eden
• 2595sq m section.
• 21 renovations since 1940s.
• $4.21 million sale last year to Compass boss Karim Hussona.
• 6-bedroom, 3-bathroom mansion proposed with swimming pool, spa, tennis court and 4-car garage.