I have created a report for an object and have a link to the report on the view page of the records of that object. I want to filter the report on the current record through which the report is opened.
Reports & Charts are meant to be used with a list of records & are not specific to a given record.
You may want to consider adding a Document Template field to the object to have template based reports specific to each record. Eg. Invoice Statement for each SalesOrder record.
Having said that, you can also filter a Report to be generated for a single record. By adding a dynamic filter on the report that filters report on the basis of Object ID field. However, this filter needs to be configured manually on each 'Report View' page, as these pages do not have any record context.