The phrase "not keen" refers to a lack of enthusiasm or interest towards something. Some synonyms for this phrase include "indifferent," "apathetic," "unenthusiastic," "disinterested," and "lukewarm." These words all convey a similar sentiment of not being particularly interested in or excited about something. Another word that could be used is "nonchalant," which suggests a relaxed and casual attitude towards the topic at hand. Ultimately, any of these synonyms could be used to describe someone who is not keen on a particular subject or activity, and can inject some variety into written or spoken language.