Go ahead and keep a secret when you really strategically need to keep a secret. Don't get emotionally attached to it being a secret though- because one day, probably soon, it'll get duplicated. And do you have a thoroughly thought out realistic business reason to keep it (temporarily) secret in the first place? Usually not in my experience.
In my experience the acquiring company will require an NDA since as a public company they would not want early acquisition discussions disclosed. I've only done one such transaction but I understand this requirement is typical.
The company to be acquired also wants to have an NDA in this case since in the event that the acquisition does not proceed you don't want your negotiating position revealed to other potential acquirers before you have chance to even negotiate with them.
I'm guessing an example would be if you are entering negotiations to be bought out by a public company.