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). An example of the last is an oft-quoted–in my family–exchange from the wonderful film (and fount of Britishisms) “About a Boy.” The Hugh Grant character, Will, is developing feelings for a woman, as Will’s young mate, Marcus, explains to the woman’s son, Ali:
Marcus: Oh, don’t worry, I think your mum is keen on him.
Ali: [shouting] She’s not keen on him! She’s only keen on me!
Google Ngram shows a roughly 100 percent increase in the use of both keen on and keen to in American English between 1990 and 2008.
Scientists are keen to explore cloning as a potential source of embryonic stem cells, which could be used to treat diseases such as Alzheimer’s or Parkinson’s. (Time, Dec. 11, 2001)/ If You’re Keen on Quinoa (New York Times headline, May 27, 2011).