There is no maximum amount. They can send you 17 trillion dollars if they have it to give you. However, any amount over $10,000 will automatically be reported to the treasury department by the financial institution in the U.S. that receives it. The Treasury Dept has nothing to do with the IRS. There is no requirement for the recipient of a gift to report it to anyone at any time for any reason. The giver of any gift over $14K in any one tax year is the one required to report it to the IRS. There's no tax assessed provided the gift is under $5.2M.

<a rel="nofollow" target="_blank" href="https://www.irs.gov/businesses/gifts-from-foreign-person">https://www.irs.gov/businesses/gifts-from-...>

A small addendum to SU Carl's reply above -- whereas there is no taxation on gifts , there is a requirement to report gifts received  from a foreign person / trust  by a US taxpayer  only when the threshold of $100,000 is reached or breached. This is done on form 3520 and I believe  TurboTax supportts it.  No taxation by the USA.  Also note that if the amount is held in any foreign account with yourself as a signatory or owner , you may have to file  the FBAR and FATCA forms

Good Luck