The phrase "not be averse to something" essentially means that someone is willing to consider or accept a particular idea or action. When looking for synonyms for this phrase, one might consider words such as "open-minded," "receptive," "amenable," "agreeable," or "accepting." Other options might include "interested," "willing," "inclined," "favorable," or even "enthusiastic." Depending on the context in which the phrase is being used, there could be a wide range of possible synonyms that could apply. Ultimately, the key is to find a word or phrase that accurately conveys the idea that someone is not opposed to the suggestion at hand.