Scotland News understands several residents have already left the building following the warning on Monday, while others are considering their options.
The complex, which contains more than 100 flats, was built on the site of a former whisky bond.
A fire in March 2024, which left two firefighters injured, rendered a number of flats uninhabitable, while several others were damaged by smoke.
A City of Edinburgh Council report later found a previous building survey carried out in May 2022 identified a series of issues, including “combustible cladding and insulation, combustible decking and internal fire-stopping issues”.
Seven internal lifts were also found to be “non-compliant”.
Persimmon put a number of safety measures in place in the aftermath of the fire, including “waking watches” and fire supervisors.
There is currently no timescale for the remediation works to be completed as the “full scope of works has not yet been finalised”.