Difference between singular and countable nouns
Solution 1:
As Færd mentioned in their comment, word in that specific meaning (the manager wants a word) cannot be used in a plural form.
Actually, having words with someone means you are having a fight with them. In that sense, words is not used in the singular.
You picked a word that has many meanings, and that is used in a lot of idiomatic expressions. Those idiomatic expressions can look very similar but still convey a vastly different meaning.