Do I have to use the preposition about or for after negotiate.For example:
We will negotiate with the company about/for a better deal.
I think your sentence is correct.
We will negotiate with the company for/ about a better deal
You can use either for or about in your sentence
Here is the link.
https://www.oxfordlearnersdictionaries.com/definition/english/negotiate
It is not idiomatic say "negotiate for/about" just as it would be incorrect to say "discuss for..."
You can discuss a topic with someone. You can negotiate a deal with someone.
Your sentence should be:
We will negotiate a better deal with the company.
I fully agree with Lambie and Astralbee.
Which preposition do I use after the verb “negotiate”?
That depends on the context, I will explain.
Do I have to use the preposition about or for after negotiate? For example: . . .
No, you don't have to use those two all the time.
For your example sentence
We will negotiate with the company about/for a better deal.
I feel the best choice would be what Lambie and Astralbee suggested: "We will negotiate a better deal with the company." Here are a few related examples:
I've managed to negotiate a five percent pay increase with my boss (Cambridge).
We want to negotiate a settlement that is fair to both sides (Cambridge).
Note how the focus in these examples are on the parties involved. Now let's look at the use of "for":
Note how in all these examples, the focus is on what you are negotiating for and not on the parties. Also note the frequent use of "negotiating".
To sum up, in your example sentence, if you want to focus on the "deal", then you can say
"We will negotiate for a better deal" or "We will be negotiating for a better deal."
and if you want to focus on the party you are negotiating with, then say what Lambie and Astralbee suggested
"We will negotiate a better deal with the company."
The use of "about" as a proposition is more rare than the use of "for".
Edit: As Jason Bassford pointed out in the comments, the prepositions "for" and "about" become more usable in your example sentence when we change the form to "negotiation" (noun), and if we rephrase the sentence just a bit.
"(1) Our negotiations with the company are for a better deal. (2) Our negotiations with the company are about getting a better deal."
negotiate takes direct objects:
We will negotiate with the company about/for a better deal.
should be:
We will negotiate a better deal with the company.
That is the most idiomatic.
Any dictionary will tell you that so I am not bothering to cite one.
It is possible to say: for a better deal but in written form that is not the best choice.
No, about and for are not the only prepositions you can use after the word negotiate.
For example, you can:
negotiate with someone/a view to (as you illustrate)
negotiate after lunch
negotiate in good time
negotiate before supper
negotiate around an issue negotiate on common ground
and so on.
It all depends on the context.