To enter into prenuptial agreement, do you have to be engaged to be married?
If jurisdiction matters, USA.
Well, it is hard to prove a negative, but the answer seems to be: No, you do not need to be engaged.
For example, the article Prenuptial Agreements in the United States from the International Academy of Family Lawyers tries to give "an overview of this rather complex area of American family law and estate planning", yet contains not mention of engagement at all. If being engaged were relevant, it would likely be mentioned.
Similarly, the "Frequently Asked Questions about Premarital Agreements" on lawhelp.org do not mention engagement.
Also see Does being engaged (to be married) carry any legal significance? for information on where being engaged does or does not matter legally.
Yes, you need to be engaged, but this is only because it is tautologically true (i.e. true as a matter of the technical definition of the term).
Consider the definition of premarital agreement in Colorado Revised Statutes § 14-2-302(5) which is based on a uniform state law widely adopted and has a definition that is consistent with the generally used meaning of the term.
"Premarital agreement" means an agreement between individuals who intend to marry which affirms, modifies, or waives a marital right or obligation during the marriage or at legal separation, marital dissolution, death of one of the spouses, or the occurrence or nonoccurrence of any other event.
The term includes an amendment, signed before the individuals marry, of a premarital agreement.
Pre-marital agreements only take effect upon an actual marriage, because the term only applies to agreements that modify of marital rights.
Thus, people who aren't married and aren't engaged can't enter into a marital agreement, because they don't intend to marry.
A formally expressed intent to marry is pretty much definitionally, what engagement means, in the ordinary sense of the word. For example, Oxford Living Dictionaries defines "engagement" in the relevant first sense of the word as: "A formal agreement to get married."
Obviously, however, if you believe that "engagement" has a meaning other than a formally expressed intent of two people to marry each other, then this might not be true. For example, if your definition of "engagement" includes a presentation of a physical token of an intent to marry, such as an engagement ring, then no, you don't have to be engaged.
People who are currently married can also enter into marital agreements, but these agreements, for obvious reasons, aren't pre-nuptial agreements. They are post-nuptial agreements.
I suppose that two people who aren't married and don't intend to get married could enter into a domestic partnership agreement that is written in such a way that it survives a subsequent marriage of the parties that wasn't intended when it was entered into. But, I'm not sure that this would properly be called a pre-nuptial agreement. This is because the terms of a domestic partnership agreement are immediately effective, rather than taking effect only upon the parties getting married, as they would in the case of a prenup.