Check the permissions. we will not give Save option to all people. In your site role your admin restricted save option.
If you get save permission then you can save it in existing workbook.
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This other thread describes a similar situation: Save button option not showing in Web Edit. Can you try the workaround suggested there?
"... click "Save As" and type in the exact name of the report in the same folder. This will give a "do you wish to overwrite" prompt..."
Most of the times, just as mentioned by Sankar, this means some permissions are set incorrectly but seeing you are a site administrator makes me doubt that.
Hope this helps!