***Neither a teacher nor a native speaker.***
Well, I've just learned the word keen.
I'm sure keen is a positive word, that's why I disagree with this sentence.
Maybe it should be:
He is very keen to visit the museum.
Let's replace keen by a "negative" word.
He is too shy to visit the museum.
Can you see the difference now?
P.S. However, I'm not fully sure here -> Confirmation would be nice!