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Related to keen: dictionary
treat them mean, keep them keen
Neglecting a romantic partner (or a potential romantic partner) keeps him or her interested in you. A: "Why hasn't Tom called me yet? I thought he liked me." B: "Maybe he thinks that 'treat them mean, keep them keen' actually works."
be as keen as mustard
To be very enthusiastic about something. Primarily heard in UK, Australia. These new kids are as keen as mustard to be in the choir, so we can definitely get them to clean up the choir room for us.
be keen about
To be excited about or interested in something. Rich is very keen about this cruise he's planned for the fall. Don't take this opportunity if you aren't keen about it.
See also: keen
be keen on
To be excited about or interested in someone or something. I'm glad that Jimmy and Lena are finally going on a date, since he's been keen on her for months. Don't take this opportunity if you aren't keen on it.
be mad keen (on someone or something)
To be very enthusiastic or excited about someone or something. Oh, I've seen the way Tim smiles at you—he's definitely mad keen on you! I'm mad keen on that college, so I really hope they accept me.
keen as mustard
Very enthusiastic and excited (about or to do something). Hyphenated if used as a modifier before a noun. There are plenty of talented kids around this area who are keen as mustard to be on the team, so we should have no problem filling the spot. Silverstone plays the hardened veteran detective, while Johansson plays the keen-as-mustard rookie assigned to be her partner.
have a keen interest in something
to have a strong interest in something; to be very interested in something. Tom had always had a keen interest in music, so he started a band. The children have a keen interest in having apet, so I bought them a cat.
keen on doing something
willing or eager to do something. Dave isn't very keen on going to the opera. The children are keen on swimming this afternoon. Shall I take them?
keen on someone or somethingand keen about someone or something
to be enthusiastic about someone or something. I'm not too keen on going to Denver. Sally is fairly keen about getting a new job. Mary isn't keen on her new boss.
keen about, be
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.
See also: keen
keen as mustardmainly BRITISH, OLD-FASHIONED
If someone is keen as mustard they are very eager to do something. I have an adult pupil who scored very low in assessments but is keen as mustard. Note: You can also describe someone as mustard-keen. Sir Richard was mustard-keen to say his bit. Note: `Keen' means enthusiastic, but is also used to mean sharp when referring to the blade or cutting edge of a tool or weapon. An acidic or sour taste can also be referred to as sharp, so enthusiasm is being likened to the sharp taste or `edge' given to food by mustard.
keen as mustardextremely eager or enthusiastic. British informal
Keen is used here to mean ‘operating on the senses like a sharp instrument’.
(as) ˌkeen as ˈmustard(British English, informal) wanting very much to do well at something; enthusiastic: She’s as keen as mustard. She always gets here first in the morning and she’s the last to leave work in the evening.
be mad ˈkeen (on somebody/something)(informal) be very interested in or enthusiastic about somebody/something: She’s been mad keen on African music ever since she came back from Zimbabwe last year. ♢ He’s mad keen on getting into the army.
mod. fine; excellent. Your idea is really peachy!