Can we do some server settings on the SSRS server by which any report is called then this will update these values to database table for e.g. I have a rdl file and a table tblLogDetails. When any user hits a print button in my application then rdl file rendered up and at the same time reportserver will update/insert tbllogdetail columns UserID, PrintTime,PrintDate, IsPrint flag a boolean value.
You could insert a specific Dataset in each report that updates your tblLogDetails table.
Just set up the dataset as you would normally, but have the proc or script update your log table.