Form 1040-NR
Form 1040-NR: the non-resident return, and why most owners here do not file one
The US personal tax return for non-residents. You file it only if you have US income the US can tax — which most foreign-owned LLCs with overseas customers do not.
Form 1040-NR is the personal income tax return for a non-resident alien. It is filed by a person, not a company, and only when that person has US income the United States is entitled to tax — most often income effectively connected with a US trade or business.
This is where the ITIN question comes from. Filing a 1040-NR requires a US identifying number, and a non-resident who has none must apply for an ITIN. So if you needed to file one, you would need an ITIN too. The two travel together.
The common case on this site is the one where neither applies. A US LLC owned by one non-US person, with no US office, no US employees and customers outside the United States, generally has no effectively connected income — so the owner generally has no 1040-NR to file, and therefore no reason to obtain an ITIN. The company's yearly obligation is the Form 5472 and pro forma Form 1120, and those are an information report about the entity, not an income tax return about you.
Change the facts and the answer changes. US-based inventory, US employees, US real estate, or customers you serve from inside the United States can all create effectively connected income, and then a 1040-NR and an ITIN come into play. That is outside what we prepare, and it is a question for a US CPA rather than for us.