As L1B Visa, not US citizen, do I need to report my own money (in a bank) that I have in my home country? And what about the money that is not in a bank account there?

[eliacim]

In the last years I've reported the money that is in my bank account there, converting to US dollars. How should be the correct way to declare/report the money in a bank account?

And what about the money that is in a safe at home? Do I need to report as well? How to proceed?

[KarenJ2]

Depending on the balance of your foreign bank account, you may have a reporting requirement.  You do not need to report cash you hold.

You potentially have two reporting requirements, The Report of Foreign Bank and Financial Accounts (FBAR) and/or Form 8938, Statement of Specified Foreign Financial Assets.

There are questions in TurboTax regarding your foreign accounts and the program will advise you if you have a reporting requirement.  If you do, you convert your currency to USD before filing.

Comparison of Form 8938 and FBAR Requirements

[eliacim]

For the cash that I hold out of a bank account in my home country, even though is more than the minimum FBAR amount, I do not need to report, right?

If I move this amount to a bank account, for the next tax report, will I have problems?

[KarenJ2]

You do not need to report cash on the FBAR however you do need to report any income received during the tax year on your US tax return.

I do not know if you could have a problem regarding an increased foreign bank account balance.  That is impossible for anyone to say.