A mortgage to a non resident is called a Foreign National Mortgage loan. A foreign national who is not a resident of the United States will in many cases seek to own real estate. Financing real estate is generally done by US mortgage companies and banks to United States citizens.
Lenders also offer loans to non citizens. They may be resident aliens, temporary residents or other classifications of either temporary or permanent status.
Foreign national mortgage Wikipedia
Down payment requirements are usually higher for foreign national borrowers. The minimum down payment is usually 20% of the total purchase price of the property. This is also referred to as an 80% Loan to Value "LTV" loan.
The most common type of Bank, Lender or Mortgage company, to offer Foreign National Mortgage loans are those in and around major cities. These lenders are situated where there is a large foreign natinional population base due to high immigration rates. The lenders in new immigration hubs are more likely to have foreign national mortgage loan programs so they can serve their local community.
The best referral source for obtaining a foreign national mortgage loan is a local real estate broker that works in a location that has a high immigration rate. Some cities that might have a real estate broker familiar with Foreign National mortgage finance or many Foreign Nationals buying real estate might be Queens, New York, or San Diego, California, etc.
Lenders do prefer a credit report from the home country, although some will take 3 credit reference letters from the borrower. The credit report is much like our own in the U.S. but without scores as their scoring systems are different from our own. There are agencies in the U.S. that obtain the data, conform it to U.S. regulations and provide the background checks (verification of employment, verification of an existence of a company for self-employed) and anti-money laundering, anti-terrorism, OFAC and red flag rules.