When a user wants to transfer the ownership of a Report to another user, they can change the Owner field on the Report and update it to the preferred user.
Users can also do this in bulk via Mass Update:
1. Navigate to List > Mass Update > Mass Updates
2. Expand General Updates
3. Select Report
4. Under the Criteria tab, add Filter:
a. Owner = previous user
5. Under Mass Update Fields tab:
a. Look for the Owner field and tick the Apply checkbox
b. Set Value to the new user
6. Click Preview
7. Review the list and Click Perform Update