There are several synonyms for the phrase "under his nose." These include "in plain sight," "right in front of him," "under his very eyes," "within reach," and "in close proximity." All of these expressions imply that something was very close to someone, but they failed to notice it. It is often used when someone misses an obvious clue or solution to a problem. One might say, for example, that the answer was right in front of them "under their nose" the entire time. These synonyms can be helpful in providing alternative ways to express the same idea and can add variety to one's writing or speech.