Collocations for keen - adj.

appear, be, look, seem, sound
remain

extremely, fairly, very, etc.
She's a very keen gardener.

desperately, especially, more than, particularly, terribly
He's particularly keen on football.

not at all, not exactly, not overly, not too
The banks were not at all keen to lend to somebody who actually seemed to need money.

equally
She is extremely keen to remain with the police and we are equally keen to retain her.

always
She was always keen to hear the local gossip.

obviously
naturally, understandably
She was naturally keen to make a good impression.

for
They were desperately keen for information.

on
Sally's quite keen on the idea.

as keen as mustard (= very keen)

Keen is used with these nouns:
admirer, amateur, anticipation, appreciation, awareness, collector, competition, ear, eye, eyesight, fan, fisherman, follower, footballer, gardener, golfer, insight, intellect, interest, mind, observation, observer, perception, photographer, sailor, sense, sportsman, sportswoman, supporter, swimmer, traveller, understanding