I came across the following sentence in a test and it is wrong answer so there cannot be a sentence in this structure. Could you explain to me why?
He is rumored that he is writing a new book.
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Because is rumored takes a choice of frames:
It is rumored that X is Y.
and, by subject raising,
X is rumored to be Y.
Your sentence is of the form
*X is rumored that X is Y.
but that is not grammatical. (As with most "why" questions, there is no genuine answer to the "why": I can only lay out the forms that are grammatical and show you the relationship between them).