A sales rep for NCI -- which sells cleanroom equipment and supplies -- tells TMZ, it received an order request on January 29 for a whopping $56.4 MILLION worth of masks from someone claiming to be tied to the Chinese government.

The rep says the order -- which was for 553,000 cases of masks -- obviously would have made the company's year, but NCI had to say no because here's the thing ... they're coming up more than a half a million cases short!

That's right, NCI says it only has about 30 cases left in inventory!!!

The reason is simple: Demand has been insanely high since coronavirus news and cases have spread. Ironically, the CDC says that crazy demand is totally unnecessary because only diagnosed patients should even be wearing the masks. If you don't have the virus, you don't need the mask.

But, since everyone's trying to get them ... we're told NCI actually doubled its price from $100/case to $200/case, attempting to drive down demand and make its supplies last.

That hasn't really worked out, and inventory is so limited now, the sales rep says they're only selling to longtime customers. Still, after the massive order request -- apparently from China --  we're told 2 more people showed up at NCI's Minnesota offices asking for 56,000 cases at the new $200/case price.

Yes, that would be a cool $11.2 mil in their pockets, but obviously, NCI had to deny that one too. Fact is, the company keeps getting "we'll pay anything" offers but you see the pattern -- they can't secure enough product.

BTW -- each case holds 1,000 masks, so the actual amount of masks in demand is in the hundreds of millions. As the sales rep tells us, "There's nobody out there that has that many masks in stock."