Can I speak to (one)?
A request to talk to someone in particular. Can I please speak to your supervisor? A: "Can I speak to Josh?" B: "He's not available right now—can I take a message?"
Could I speak to someone?
and Can I speak to someone?; May I speak to someone?the phrase used to request to talk to a particular person, usually on the telephone. (Also used with talk in place of speak.) Tom (answering the phone): Good morning, Acme Air Products. With whom do you wish to speak? Bill: Can I speak to Mr. Wilson? Tom: One moment. Sally: May I speak to the manager, please? Clerk: Certainly, madam. I'm the manager.