I'm not quite clear on what you're asking but PPL has nothing at all to do with CFI privileges.

You need a CPL (or ATP) in category/class to get the corresponding CFI rating.

If your ASEL cert is just PPL, then you'll need to upgrade that to ASEL CPL or ATP. Since you already hold an ATP it's no big deal to do an add-on, although I suppose you could do an ASEL CPL checkride if you wanted to.

Without looking at the PTS, I suspect it might be fewer manuevers to do the ATP add-on.