Employees at the engineering plant in Inchinnan were told of the cuts yesterday.
The firm said that it would offer a voluntary redundancy option to workers and hoped to avoid compulsory cuts.
The company, which specialises in aeroplane engines, announced in 2012 it was closing its plant in East Kilbride and transferring jobs to the Inchinnan factory.
That move has not yet been completed, with the East Kilbride plant set to close in 2015.
Chris Cholerton, Rolls-Royce's executive vice-president for compressor components, said: "It is never an easy decision to propose reductions in our workforce, but it is a sign of the increasingly competitive market in which we operate that such actions are necessary.
"We have invested over £85 million at Inchinnan to make it a state-of-the-art facility and are continuing to transfer our operations from East Kilbride to maximise efficiency.
"This will ensure we remain competitive and are best placed for any opportunities that may appear in the future."
The cuts will affect staff from the shop floor up to senior management.
Derek Mackay, the MSP for Renfrewshire North and West, said: "This will be worrying news for all those working at Inchinnan and their families.
"I have spoken to the Finance Secretary and have been assured that the Partnership Action for Continuing Employment team will be available to support anyone facing redundancy and that the Scottish Government and Scottish Enterprise are in contact with Rolls-Royce.
"The plant has been a success story and I will be looking to meet the management as soon as possible to discuss their continued presence in the area."