The unit has most recently been used as a ticket office.
Dundas Heritable Investments is seeking permission to turn 3 Dundas Street - known as Dundas House - into a cafe.
The unit, which sits opposite Queen Street train station, has been used as a ticket office for ScotRail - the upper floors are used as office space.
A separate application for the alterations shows that the cafe would be called ‘Kaffateria’.
The cafe would have capacity for around 60 customers.