A high school diploma or the equivalent qualification is the minimum requirement to study the Korean language on a student visa at a Korean University KLI. The student must also show a Certificate of bank deposit balance over $10,000(USD).
Most schools have no official age limits, but it might be harder for older students to get accepted. The school will look closer at your purpose for studying in Korea and your CV to see what you have done after graduation.
If your nationality has a record of abusing visas to Korea the migration authorities might not issue a student visa to older students. However, I am not aware of any official documents stating which nationalities are affected by this.
The cheapest university KLI that we work with is Yeungnam University outside Dauge where you can take a one year language course for 5 250 000 KRW. We can help students from Europe, the Americas and Oceania to apply to selected Korean Language Institutes. Fill out our information request form if you want help.
Read more:
Korean Language Classes in Korea
Study in Korea
Student visa to Korea