Sorry, no. The subject is always in the subjective case: he, she, it, we, you, they, who, whoever. It is the object which takes the objective case: him, her, it, us, you, them, whom, whomever. So “whoever it is” is correct.

Actually, in this instance it doesn’t matter whether “whoever” or “it” is the subject of the clause, because the verb to be doesn’t take an object, it takes a complement, which is always in the subjective case anyway. Hence “it is he” is correct, “it is him” is not.

Well, that’s what was (still is?) taught in traditional English grammar, which is modelled on the classical languages Latin and ancient Greek. In those languages distinctions of case are vitally important. It is debatable whether the classical rules apply to English. Hence, many English speakers say (and write) “it is him,” although pedants (like me) prefer “it is he”. Consider the following from the Gospel of John (18:4–5a) in a modern English translation (NIV):

Jesus, knowing all that was going to happen to him, went out and asked them, “Who is it you want?”
“Jesus of Nazareth,” they replied.
“I am he,” Jesus said.

(Note also the use of “who” in “Who is it you want?” If Jesus had used the verb to seek instead of the verb to be, it would have been “Whom do you seek?”)

But anyway, “whomever it is” just sounds wrong!