Evenlode Tower in Blackbird Leys is one of two high-rise buildings owned by Oxford City Council where cladding failed fire safety tests.
The authority is looking for mast climbers - a type of moveable platform - to enable cladding to be removed.
An Oxford City Council spokesperson said it was "awaiting a timetable" for when the process could begin.
Cladding removal has started on Windrush Tower - the other Oxford City Council high-rise where cladding failed tests - because mast climbers were already in place for a refurbishment project.
'Pressure on suppliers'
Cladding on 137 high-rise buildings across 41 local authority areas in England has failed fire safety tests, according to the latest figures.
Oxford City Council said it had no confirmed date for installing new cladding on the Evenlode and Windrush towers.
It expects "pressure on suppliers" could lead to increased delivery times and said residents would be the first to know once a timetable was agreed.
Oxfordshire's fire service has said residents are safe to remain in the towers, which both have sprinkler systems fitted.
A council is searching for equipment to enable contractors to remove unsafe cladding from a tower in Oxford.