I've had this situation happen several times....
You can purchase if paying cash but as the others stated it may be very difficult to get a loan.
The first problem that may come up is the fact that when your credit is pulled, it may come up that you show no credit score or trade lines (and most lenders want to see an established history of trade-lines). Secondly, there are regulations relating to purchasing property if you are not a US citizen. Keep in mind that there are tax-advantages when you purchase a property when you ARE a US citizen. I recommend consulting with your accountant for specific details.
Feel free to contact me if you have additional questions.
-Amy S. Arey, Realtor
Halo Group Realty, LLC