Julie Kelley, the Yorkshire official of the UCU said staff were being told of plans over three days this week.
She said: “We have been told that they are having to find savings of £9m from September and another £1.8m after that.”
She said the union was now braced for a raft of redundancies and that it was expected that the college would open up voluntary redundancy.
The college confirmed that it was holding briefings with staff about its business planning for 2015 in light of a “large decrease in funding.”
Mrs Kelley said the college was considering closing its smaller community venues.
She said the cuts were being made because of major cuts to in non-apprenticeship adult skills budget and a reduction in 16-18 year old learner funding.
A statement from the college said: “Leeds City College has in recent years made significant changes to help sustain its financial viability and growth for the future.
“On-going reductions in public sector spending has meant the college has had to continuously review its business operations and evolve to meet the needs of a changing and challenging environment in a climate of continued government funding reductions, while meeting a requirement to provide an enhanced, inspirational learning environment for students. In 2015, Leeds City College is again faced with a large decrease in funding and is this week (from the afternoon of Wednesday) holding briefings with staff with regards to a review of its business planning.
“The college cannot comment further on any specific issue or outcome until staff have been fully briefed.”