The Pennine Bakery in Shaw, which employs 174 people, has been operated by Warburtons for over 40 years.
The company said it had started a 90-day consultation and hoped to find alternative jobs within the group for as many staff as possible.
But compulsory redundancies have not been ruled out.
In a statement, Warburtons said: “This very difficult proposal has been made to support the future of the business by enabling us to produce and distribute our products more efficiently.
“If the closure is implemented, we will do everything we can to minimise redundancies and wherever possible will find alternative jobs within the business.”
The company insisted it remained profitable but was responding to tough economic conditions.
“As a family business, we have a responsibility to make sure we are in the best possible shape for the future so that we ensure our business is efficient and continues to be profitable,” the statement continued.
“To do this we have to take some tough decisions, but are committed to working closely with our affected employees to explore all the available options.”
Md Robert Higginson added: “To close a bakery is the most difficult decision a family firm like Warburtons can take. We appreciate how tough a period this is for our employees in Shaw and we will work closely with them and their representatives to discuss our proposal and explore all available options.
“The proposed changes are designed to improve our manufacturing and distribution operations, which will help us better meet the demands of our customers and consumers across the UK.”
The Bakers, Food & Allied Workers Union reacted with dismay, accusing Warburtons of putting profits ahead of the wellbeing of workers.
Warburtons operates 15 bakeries and employs some 5,000 people. Its nearest facilities to the Oldham plant are in Bolton and Burnley.