Is there a way to add a custom field to the Ownership Transfer Record? I don't see it available as a transaction field or an other record field.

I dont think so, not without scripting

@Mika Hakkinen is it possible to add a custom field to a record via script even though it's not possible in the UI?

Also @Mika Hakkinen if I create a scripted field can that scripted field be used in Saved Searches? or is it only avialble when viewing the record?