The Custom Field column does not know anything about the context of your Custom Fields. The column does have a field type option where you can tell the column what type of content your custom field contains. This may alter the inline edit behavior, but it will never become a select box, it does not know where to get the options.
But if you use a plugin to create your custom fields like ACF, Pods or Types, you can use the specific integration add-on for these plugins. In that case, we do know the context of the custom field. So for example, if you have a select field created with ACF, you can create an ACF column for this field with the ACF integration add-on and inline edit will automatically become a select field.
If you created the context of your custom fields yourself, you can use one of our filters to change the text field for Inline edit to a select box. The following documentation page contains the filter with an example that does exactly what you’re trying to accomplish.