This will not exactly achieve your stated goal, but it may be an acceptable alternative.
Create a file on your desktop with the name of the file you do not wish to be created. It does not need to have any content, it can be 0 bytes. Right-click on the new file and select Properties. Mark the boxes for "Hidden" and "Read-only". Click OK.
The file now exists, but it is a fixed size and should not appear on your desktop. Attempts to create a file with that name will result in an error.
I'm not certain what effect this will have on the program that is creating the undesirable log file. It may throw an error message, it may hang, or it may just go on as if nothing is different. In any case, I suspect the problem would be the same or similar for any method you may find of preventing the file creation.