The type of file being discussed does not usually fit the DVD format but if the purpose is just data storage, it may be possible but not desirable. A program called InCD or something similar to InCD might, but there are more problems with those type programs than they are worth. As far as I know, they are no longer supported because of that.
BTW: Assuming the reasoning for this is to hide something, the computer will still make a record of the activity no matter what was done with the file.
Is there any software out there that allows you to download video's and/or music straight from the internet to a DVD or CD without said file saving on your PC/ laptop ?