Nginx cache gzip file's to temp directory?

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Job Description

Is the following possible through Nginx:

I now have gzip on; but the server needs to compress the popular files everytime, the files are xml files created through a database, but they are "static". I know I can set gzip_static on; but there are no .gz file ofcourse.

Is there a way I can let Nginx save the gzip file's it creates and save it to cache/temp directory for future use?