I haven't been able to locate any reports providing estimates on the number of non-US citizens who work remotely from abroad for US companies. I understand that this data may be inherently elusive, but I was hopeful of finding some rough estimates regarding the market size.
Almost all big tech companies have offices in many parts of the world so they would all count as "non US citizens employed by US companies". Many smaller companies also do that because they cannot always afford to pay US equivalent salaries but can find talent in other parts of the world at a much cheaper rate (and No, cheaper is not always worse. Sometimes it is just about cost of living and other benefits that people are looking for ).
I don't have numbers, but in my experience I'd say "a lot." The freelancers I know try to get US customers because they get paid more.
Companies may hire remote non-citizens as contractors because that avoids any real or perceived labor law, visa, and tax issues. If they have actual employees in other countries most likely that's through a branch office.
I think most of the remote non-citizen employment happens through what we call offshoring. US companies contract with software shops and agencies in low cost of labor countries with no huge language barrier -- India comes to mind. The people doing the work aren't employees or freelancers, they are like factory workers making shoes for Nike in Vietnam, employed by a local company that contracts out for work. With that setup only the managers need to speak English.
It's sort of like, when a British person lives in America they're an "expatriate", but if an Indian lives in America they're an "immigrant".
Just the way the world spins.
(Off-topic non-relevant story follows)
I once flew Air India from New Delhi to Chicago. 15 hour non-stop run. At O'Hare, as we were exiting the airplane the airport (airline?) staff waiting to pick up the wheelchair passengers were saying random words loudly in mock Indian accent and laughing.
I wonder how they greet passengers disembarking a Lufthansa.
I don't know if there is a number somewhere but me and most of my peers that live in Latin America that achieve certain level of proficiency we all work for Us or Europe and not for our local economies
This would be very easy with a simple tax change. Outsourced salaries are no longer deductible as a business expense. Right now, taxpayers subsidize outsourcing.