U.S. Immigration Services doesn't require anybody's signature to be notarized on an I-9 form. There is no notary language included on the form, nor space to put the notary stamp.
But maybe your new employer, based in another state, needs somebody to verify your ID and help you complete the I-9 form. They probably told you to "find a notary to do it." They might have even said to "get it notarized" and gave you piece of paper with "instructions to notary."
However, verifying a person's ID for employment in the U.S. is not a notarial act, duty or obligation, and getting your ID verified for right to work in the U.S. is not a "notarization."
That said, somebody who just happens to be a notary can look at your IDs and complete Section 2 on your I-9 form. In fact, anybody designated by your employer can perform that task. If this is the case, your company should provide writte n authorization to whoever completes section 2 on your I-9 form, whether that person is a notary or not.
If somebody happens to be a notary, it doesn't necessarily mean anything is being "notarized," stamped with a seal, or that the notary will write "Notary Public" as their title. Because whoever completes section 2 becomes personally involved in the document, and it's not legal for a notary to notarize signatures on a document they are personally involved with.
So the only choice I have is to act as a Notary Public and notarize your signature, or act as a representative of your employer and sign my name as somebody who verified ID. It's not legal for me to do both.
Unfortunately, most out-of-state employers do not understand this, and write their "instructions to notary" asking to both verify a new employees ID and notarize their signature. In that case I have to say no.