SBIR grants are intended for small, for-profit businesses, that are at least 50% owned by US citizens or US permanent residents, with the primary place of business inside the US.
The SBIR.GOV website has a full set of FAQs on eligibility requirements for "Small business concerns". In particular, they define "small business concern" as follows.
"A Small Business Concern (SBC) must satisfy the following conditions on the date of award for both Phase I and Phase II funding agreements:(1) is organized for profit, with a place of business located in the United States, which operates primarily within the United States or which makes a significant contribution to the United States economy through payment of taxes or use of American products, materials or labor;(2) is in the legal form of an individual proprietorship, partnership, limited liability company, corporation, joint venture, association, trust or cooperative, except that if the concern is a joint venture, each entity to the venture must meet the requirements set forth in paragraph (3) below;(3) is more than 50 percent directly owned and controlled by one or more individuals (who are citizens or permanent resident aliens of the United States), other small business concerns (each of which is more than 50% directly owned and controlled by individuals who are citizens or permanent resident aliens of the United States), or any combination of these; and(4) has, including its affiliates, not more than 500 employees. (For explanation of affiliate see www.sba.gov/size(link is external)).For SBIR program only: Some of the 11 federal agencies administering SBIR awards may choose to issue a portion of their awards to firms that are majority-owned by multiple venture capital operating companies, hedge funds, or private equity firms. You can see which agency is currently using this authority here."