the sentence in question: "I know who I am calling next time...."
or
"I know whom I am calling next time....."
Whom is the appropriate grammatical word
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Whom is the correct word because it is the object of the sentence. I is the subject and know is the verb. This can be a complicated rule to remember. Even as a native speaker, it took me quite a while to learn this rule. You may find this article on whom vs who use