Plans have been submitted to replace the former Robert Dyas unit into a Rituals store.
Rituals sells home and body products and cosmetics and was founded in a basement in Amsterdam 25 years ago by a group of friends.
It has shops across the country, including at West Gate in Southampton, Winchester and Portsmouth as well as several airports. It will be the first shop in Dorset.
The business has submitted a planning application to change the shopfront to the now empty Castlepoint unit, and BCP Council will decide in due course.
Rituals declined to comment.
Hardware retailer Robert Dyas closed down earlier in the summer and the unit was split into two.
At the time, centre manager David Pickett said negotiations had been taking place with future operators.
In recent months, TUI, Mango and Hotel Chocolat all opened a shop.