Dic: have a word (of something) with or for someone

4. [N-SING] a N △ If you have a word with someone, you have a short conversation with them. (SPOKEN)

• I think it's time you had a word with him...
• James, could I have a quiet word?...

3. have a word: [especially spoken] to talk to someone quickly, especially because you need their advice about something or you want to tell them to do something.

• Could I have a word? 
• [have a word with] I'll have a word with him and see if he'll help.
• [have a quick/brief word] I was hoping to have a quick word with you.
• [have/exchange a few words] Could I have a few words with you?

..... COBUILD, LDOCE

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Let's look at how different the situations are.

• My boss wants to have a word of advice with me about you.
• My boss always has words of advice for me.
• (...) in the end the Fed decides monetary policy according to its own views about the nation's economic interests. As a result, the Fed sometimes comes into conflict with the executive branch. Almost every president has words of advice for the Fed. When Fed policies clashes with the administratin's goals, presidents occasionally use harsh words.

Preposition for has a meaning of offer. :

cf. 5 [N-COUNT] N of n △If you offer someone a word of something such as warning, advice, or praise, you warn, advise, or praise them.

• A word of warning. Don't stick too precisely to what it says in the book...