Varies in meaning according to context, and preposition. Thus keen to+verb, and keen by itself as an adjective both mean, roughly, eager. Keen on+gerund or +noun means enjoying that activity or thing, while to be keen on a person means to fancy him or her (in the British sense).

What preposition is used with keen?

In 10% of cases keen for is used

You can be too keen for the job. They are very keen for this project. Management are keen for the boys to meet before Friday's gig to stop any confrontation. I like to chat with them all you see, and they were keen for me to stay in the village.

Do we say keen on or keen in?

Keen to + base form of verb. The "to" + verb is the infinitive form. Keen on + present participle: This is the gerund form.