I am a neither a permanent resident nor a US citizen. I have a bank account with a leading US bank which I use as my salary account. Income taxes are deducted at source. I know that I need to submit FBAR for foreign accounts totaling above $10k. Is there any such upper limit for money that I can keep in my US account?
There's no limit, from the legal perspective (with regards to the US law, that is), to how much you can keep on your bank accounts anywhere in the world. FBAR requirements are reporting requirements, they don't limit how much you can keep in the accounts, they only make you report the accounts to the government. There's no such requirement with regards to the US domestic accounts.
That is for the US government, your own government (of the country of which you're a citizen of) may have limitations on what accounts you may have outside of that country, or have reporting requirements of their own.
That said, keep in mind that FDIC only insures up to $250K per person (i.e.: on all your accounts) in each institution. So if you have more than $250K in a FDIC insured account - you better spread it across different banks.