An idiom or phrase for when you're about to be ill

"come down with something"

As defined by the Cambridge Academic Content Dictionary:

to catch or show signs of an illness

To complete your sentence: I'm sorry I can't come for dinner tonight because I am coming down with something

Use the tenses of "come" to suit your needs...

I'm feeling under the weather

Is a phrase I tend to hear a lot.

Definition in the Cambridge dictionary

"fighting off a bug"

I'm sorry I can't come for dinner tonight; I'm fighting off a bug.

It suggests that you have in fact caught something, has the implication that you may be infectious, but that you haven't yet succumbed to the infection.

I can't come for dinner tonight because I feel (a bug|a cold|the flu) coming on.

This is a commonly used expression (e.g. this Google result) however, I can't seem to find an authoritative reference to the usage of the expression. Going between the OED and Dictionary.com, it seems that the phrase is using two slang terms together; bug to mean the illness, and coming on to mean developing.

I know I have heard it and used it since I was young, but I'm surprised that it hasn't been authoritatively defined yet.

HTH.