The Phase 2B project will involve the partial demolition of the existing 7-storey cardiac building down to the fourth floor.
The plan is to rebuild to eight storeys aligning floors with the remainder of the adjacent hospital.
Demolition specialist John F Hunt and Bam Construction, who delivered the phase 2A Morgan Stanley Clinic, will start out as favourites for the next phase.
It is estimated the project will cost £50m, including the fit-out and replacement of all M&E plant.
Hospital staff will continue to have access to the lower building throughout the 33-month contract.
The invitation to prequalify for the project is due to be advertised next month, with tenders invited in August for a start 12 months later.