I thought he said the plane would be donated and put on display at his presidential library when his term was over which indicates to me that it's not DoDs.
Presidents can't accept personal gifts like that, especially from foreign countries. If Trump did accept a luxury plane from a foreign nation, I'm pretty sure articles of impeachment would already be drawn up.
I wouldn't be surprised if it's all a hoax and there's no plane, Trump just seeded that to the fake news media to give them something to snap at.