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The general policy of the Central (Government) Bank of Honduras is to restrain the private banks from opening Accounts to Foreigners that DO NOT have a Residency Permit.
That, however, is sometimes done with the approval of the Bank's Manager if The Client (You) shows a good banking history and the purpose of the account (Savings) is stated for support.
If the account is opened to your name, then You will be allowed to send funds by International Transfer (SWIFT).
I'd advice that You obtain some information from an American Attorney and/or Accountant in regards to how that account may be reflected on your Tax reports and some additional on the FATCA.
You may read
Regards from La Ceiba!!

Thanks Jorge for answering this question as it has been brought up a few times.

Hope this what she needed

Cheers

Honduras has some strange ways when dealing with banks here. For Instance I had an account with LaFise for 10 years. I deposited a check from the usa and they said i had to wait a month before I could access the 250 $ check I deposited. I could not use my Lempera account as they canceled it after 3 months of inactivity. Now I check my account after 5 weeks and I only have 180 $ from the  250 $ check!? I ask them how this is possible as I never withdrawn anything from it. thinking I was robbed.

OH they said we charged your account for the last 4 years of inactivity! Now I did not have no confirmation that I even had a dollar account. No bank book nothing! though they cancel my limpera account after only 3 months of inactivity (the reason it was inactive for that long was because my account card would not work) and leave another account open for 4 years without contacting me just so they can charge me?

That was the last straw, I shut my accounts down immediately. That is when they first printed me up an account book so I could sign it to show they gave me one. Im order to close the account.

beware !