Looking on the internet deeply has found these results:

I WILL NOT NEED is the most popular phrase on the web.

I WON'T BE NEEDING 1357,000 results on the web	I WILL NOT NEED 12,650,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
As it turns out, I won't be needing your services, Keith. I won't be needing you after all. William, I won't be needing you tonight. But I won't be needing emeralds, so the coat can wait until my return. I won't be needing your services after all, gentlemen. Secret service is here. I won't be needing you. I won't be needing the dress.	But in the future, I will not need this, this... No, I will not need any breakfast. If Terumichi is alive, I will not need a return ticket And since I will not need to eat again... Mr President, Commissioner, ladies and gentlemen, the progress of the discussion so far means that I will not need the five minutes allotted to me, which is good news I'm sure. I will not need to add texts manually. Mr President, ladies and gentlemen, first of all, I would like to reassure you that I will not need the full ten minutes that have been allocated to me. Mr President, I will not need the five minutes as my esteemed colleagues have covered the most essential parts of the report.

I WON'T BE NEEDING

1357,000 results on the web

I WILL NOT NEED

12,650,000 results on the web

More popular!

But in the future, I will not need this, this...
No, I will not need any breakfast.
If Terumichi is alive, I will not need a return ticket
And since I will not need to eat again...
Mr President, Commissioner, ladies and gentlemen, the progress of the discussion so far means that I will not need the five minutes allotted to me, which is good news I'm sure.
I will not need to add texts manually.
Mr President, ladies and gentlemen, first of all, I would like to reassure you that I will not need the full ten minutes that have been allocated to me.
Mr President, I will not need the five minutes as my esteemed colleagues have covered the most essential parts of the report.