keenadjective
It seems the current government is quite keen on increasing taxes.
The classes that students are most keen on fill up quickly during the enrollment period.
I wanted to go skydiving, but my husband's not too keen on it.
keen on someonemainly UK
very interested in someone, especially romantically:
He's rather keen on a girl in his school.
I think they're pretty keen on each other, if you ask me.
Seekeenadjective
I was pretty keen on her, but she wasn't all that interested in me.
She's definitely keen on him.
With his ability to strike reliably from long range, it's no longer that Chelsea are keen on him (= interested in having him play for their team).