1
general::
Be enthusiastic about. For example, He's been keen about this whole endeavor for a long time. It is Also put as be keen on, which has the additional meaning ‘‘to be ardent about or in love with," as in Jim's been keen on Jane for years. With other adverbs, such as keen at and keen of, keen has been so used since the early 1500s; the current locutions, however, date from the mid-1800s.
American Heritage Idioms
2
general::
Phrase(s): keen about someone or something
Go to keen on someone or something.
McGrawhill's American Idioms And Phrasal Verbs