I am an American Citizen moving to Argentina and will continue to work for my US based company. Should I be paid offshore to establish the foreign earned income exclusion or it does not matter?
As a general US income tax rule (e.g. §861(a)(3)), if the payment is due to services actually performed in another country, then the location of the bank or branch taking your salary is not going to be relevant. Go ahead and take your compensation in the US, if that is convenient for you.
This is particularly important for working in a country with the economic, political, and legal instability of Argentina, which has had no shortage of banking and currency issues. So most of your assets, including your direct deposit, can be held in non-Argentine accounts if that is more convenient for you.