I don't know what database you are going to use, but a table does not contain a drop down. Populating and showing the dropdown when the user is inserting new data, has nothing to do with the database design.
If a reference is another client, then referredBy will contain a clientID, and thus becomes a foreign key to the client table itself.
A second table (Referral) is needed if a client can have more than one referral. That table will contain at least two fields:
clientID
referredBy
Together they're the primary key, and both are foreign keys to the Client table.
In this case, there will be no referredBy field in the Client table.