Yeovil College and Yeovil District Hospital want to start teaching 14-19-year-olds social care skills as part of the government's Career Colleges Trust.
Initially the courses would run at its Mudford Road campus, but would eventually switch to the hospital.
Principal John Evans said they needed to secure funding for the project.
Mr Evans said the course would address the "future skill need of the hospital", which is currently having to recruit from Portugal and Spain.
Yeovil District Hospital chief executive Paul Mears said: "The career college approach could help to address our evolving workforce needs and equip local young people with the skills and hands-on experience needed to succeed and provide exceptional care in the NHS of tomorrow."
A nursing course set up by a college in Somerset could help address the "future skills need" of a local hospital, bosses have said.