There may be cases when a table is not showing up when searching for it on a drop down list. An example would be trying to create a report off the Problem table. (See screenshot below)
Navigate to the dictionary record for the table that is not showing up and search for where Type is Collection. Open the record, check to see if Active is checked. If not, then check Active.
In the case that the active field is not on the form view, the ServiceNow admin or user will need to add the Active column on the list view. Once the Active Column has been added, change the Collection record from false to true. (See screenshot below)
In the case that table Collection is set to true and the table is still not on the drop down. The user might not be in the correct scope.
Please refer to this KB article: Scoped table is not appearing as an option for a Table Name Field