Summary:

Approver Name cannot be added as a filter to a report as this field is dynamic and is situation based. When there are multiple approvers in the Approval Path, there is no definite logic to determine which Approver Name is to be filtered out. Also, if a Timesheet/Time off/ Expense sheet has been approved by multiple approvers, there would be duplicate entries in the report, as the same entry would reflect under each approver.
 
Workaround:
Run Timesheet status report ensuring that approver name is selected. Then group it by approver name.