The White House and state department declined to comment on the matter but denied a report in the Israeli newspaper Haaretz that Ross was being removed from his job.
Haaretz reported earlier on Monday that Iranian officials had objected to his Jewish background and his purported close ties to Israel.
Ross also raised the possibility of military action against Tehran in Myths, Illusions, and Peace, set to be released next month, Haaretz reported.
The move comes amid rising political tensions in Iran, where disputed elections have sparked street protests in which at least one person was killed after police fired shots.
Ross also rejected the idea of a link between the Israeli-Palestinian conflict and other conflicts in the region in the new book, a position that puts him at odds with the White House.
"There have been dozens of conflicts and countless coups in the Middle East since Israel's birth in 1948, and most were completely unrelated to the Arab-Israeli conflict," Ross wrote.
"In short, the argument of linkage has profoundly misled US policy-makers who embraced its logic and the assumptions that underpinned it," he said.
Ross, who worked on the Middle East peace negotiations under two previous presidents, is set to resume the role at the NSC, focusing on their regional impact, Haaretz reported.