There are currently several banks with the capabilities to offer ITIN mortgages. A lot of them do make you put a lot of money down. There are a few out there that have low down payments.
If you are interested in obtaining an ITIN mortgage or purchasing property, feel free to contact me and I can help you with more information.
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If you are a mortgage broker/loan officer and are interested in a list of banks that offer ITIN mortgages contact me and I'll be glad to send you a list of banks that wholesale.