By default when you export and then download the data it goes directly to the users download folder on their local computer. Which makes sense.
I am not aware of any setting that you could change to put it somewhere else. And if there was it would most likely be a global change and affect all users and all exports. Which you probably would not want.
NPrinting might be an option. But you would have to purchase that.
You could check Qlik Branch to see if there are any extensions out there that might give you this option.