No, short interest is the number of shares shorted.
I subscribed to a trading service at one time. This service shorted parabolic moves. Their advice was to reserve shares to short in advance of an actual short trade in the event that xyz happened. I only made a few long trades that were recommended by the service.
I think the service was on the up and up but never called my broker to check on reserving shares. That is why I said "second hand".