The firm opened redundancy talks with its 38 remaining tower and crawler crane drivers at the end of July, blaming the downturn in construction.
According to a report on crane website Vertikal, Kier has sent a letter to employees which explained it would no longer directly employ crane operators.
Instead the hirer plans to source operators when they are needed from employment agencies.
Kier said the decision had been forced by fierce competition on rates caused by falling demand.
Subject to the outcome of the consultation process with each employee and their representatives, all operators could be made redundant.
Kier said it would consider any alternatives that may come out of talks with construction union UCATT.
At its peak, Kier Plant employed around 80 operators who were used by Kier Construction and hired out to other contractors.