WY and NM don't have STATE tax reporting for LLC that own assets out of WY and NM.
If your US disregarderd entity has non US income, you may still have to report them. You may not have to pay taxes on them if none of your income is connected to a US trade or business, but there is reporting at the FEDERAL level of what your US entity owns worldwide, including the dreaded FACTA︀ compliance.
If the LLC is more than 25% foreign owned, it has to file form︁ 5472 if there have been any “reportable transactions” during the previous tax year (Formation and︂ dissolution filings are considered to be reportable transactions). Not filing this form will trigger a︃ $25,000 fine.
The main question will be for your CPA to rule if your income︄ is or is not connected to a US trade or business for the purpose of︅ US tax assessment.
Also, disregarded entity means that all the income are passing through to︆ the owner and has to be reported on the owner tax return directly.
If your︇ entity is not disregarded for tax purposes, it will have to file and pay FEDERAL︈ US taxes in all case.