Looking on the internet deeply has found these results:

I have no idea is the most popular phrase on the web.

I have not an idea 1884 results on the web	I have no idea 1168,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
However I am now so depressed that I have not an Idea to put to paper–my hand feels like lead I have been but half a friend to her; and if she were not to feel this disappointment so very much, I am sure I have not an idea of any body else who would be at ... I have been but half a friend to her; and if she were _not_ to feel this disappointment so very much, I am sure I have not an idea of any body else who would be at ... ... wait even till tomorrow and yet it is and unpleasant numbness ... May 2, 2014 ... I have not an idea. They are correct, although we would normally use do in these negative sentences: I do not have a clue. I do not have an ...	I have no idea how this happened. I have no idea, Your Honour... And now I have no idea why. I have no idea how to continue. I have no idea, Corporal. I have no idea who I thought I was. I have no idea what the police are... But I have no idea what to take.

I have not an idea

1884 results on the web

I have no idea

1168,000,000 results on the web

More popular!

However I am now so depressed that I have not an Idea to put to paper–my hand feels like lead
I have been but half a friend to her; and if she were not to feel this disappointment so very much, I am sure I have not an idea of any body else who would be at ...
I have been but half a friend to her; and if she were _not_ to feel this disappointment so very much, I am sure I have not an idea of any body else who would be at ...
... wait even till tomorrow
and yet it is and unpleasant numbness ...
May 2, 2014 ... I have not an idea. They are correct, although we would normally use do in these negative sentences: I do not have a clue. I do not have an ...