There's no definitive FAA statement one way or another that I could find. Outside the US and per ICAO, "take-off" is only used when accepting a take-off clearance and you should use "departure" in other situations.
There's nothing I could find about departure vs. take-off phraseology in the P/CG or AIM. The ATC orders 4-3-1 do mention it, in the context of clearances:
4−3−1. DEPARTURE TERMINOLOGY
Avoid using the term “takeoff” except to actually clear an aircraft
for takeoff or to cancel a takeoff clearance. Use such terms as
“depart,” “departure,” or “fly” in clearances when necessary.
The AIM uses "departure" in its examples but makes no comment about avoiding "take-off" and an FAA runway safety publication doesn't have anything to say about it either. AOPA has an article (from 1999, admittedly, so perhaps it's now considered outdated) that says that pilots can use "take-off" to tell ATC they're ready:
When you're ready for takeoff, use the same "who, where, and what"
format for your initial call to the tower - "Anytown tower, Trainer
zero-zero-zero-zero-Yankee , ready for takeoff Runway three-three."
That phraseology is commonly used at my local airport in the US but it would be a major no-no in South Africa, where I learned to fly. And Jon's answer is based on UK experience (only because it's in his profile), so it looks like an ICAO vs. US thing, at least to some extent.
And indeed, ICAO document 4444 uses the word "departure" as part of "preparation for take-off", and "take-off" itself for "take-off clearances" (see sections 126.96.36.199 and 188.8.131.52). 184.108.40.206 says that pilots only need to say "ready" to inform ATC that they're ready for departure: "Tower, N12345 is holding at 18, ready". It doesn't address uncontrolled fields, but the usual call I was taught was "N12345 is departing runway 18".