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I would like to know whether the following is correct:
Someone is knocking on your door.

Who could it be?

As far as I know, modal verbs do not change its form in reported speech:

He asked who it could be.

After the knocking on the door has finished, you ask yourself:

Who could it have been?

Do I get it correctly?

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Who could it have been? Yes, this is correct. – cornbread ninja 麵包忍者 Jun 17 '12 at 14:35

As long as it is obvious that the person is likely to still be standing there, it doesn't matter if the actual knocking has finished or not. You would ask yourself:

  • Who could it be?

If, however, you ask yourself the question some time later (when it is clear that the person is no longer at the door), then it needs to be:

  • Who could it have been?

In the unlikely event of you being only interested in the knocking and not in the identity of the person, then it would be correct to say:

  • Who could it have been?

immediately after the knocking stopped, even if the person is still likely to be standing there.

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If by you in You would ask yourself you mean you or Pietro, perhaps your examples hold up, but if by you you mean me, none do. In the three cases I'd ask "Who is it?" or "Who can it be?"; "Who was it?" or "I wonder who it was?"; and "I wonder who it was?" or "I wonder who it might have been?". – jwpat7 Jun 17 '12 at 22:16
@jwpat7, You are right that there are several ways of responding to a knock at the door. Perhaps I should have worded my answer as follows: "If you are going to use the modal 'could' in your response to the knock, and there are legitimate reasons for doing so, then you would use 'could be' if ... ." – Shoe Jun 18 '12 at 5:04

I agree with your first and last, but I think the modal form can change in reported speech depending on the sequence or simultaneity of events.

The asking is happening now and so is the knocking:

He asks who it could be.

The asking happened in the past and the knocking happened at the same time as the asking:

He asked who it could be.

The asking happened in the past and the knocking is an event prior to the asking:

He asked who it could have been.

As an aside, I'll assert that when you say "Who is it?", you merely want the person's identity. "Who could it be?" implies extraordinary circumstances: ordinary people wouldn't be knocking. What sort of people knock at this hour? Emergency personnel? Pirates? (I'm exaggerating a subtlety to make my point.)

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