Of Homer's two works, the Odyssey is easily the more adaptable. I was just reading that a studio is going to make a version set in space. (The article messes up which story comes first which doesn't speak well to the education of the author or the editors.) Could you do the Iliad in space? Not easily. The whole book is about very personal battles overseen by the gods. Fighting in spacesuits or spaceships would ruin that.
Where else could you put the Iliad? When could you put it? The story wouldn't work in either of the world wars, far too impersonal. It wouldn't work in the cold war, the combat is up front and in the open, not shrouded and indirect. Frankly, I think it almost has to stay in the spears and sandals era. A mob story? Maybe, but it would be a stretch.
Ok, let's turn the question around. What story could you create using the Iliad as an inspiration? The Odyssey has been a huge inspiration. Every road trip adventure story owes it a debt as does any story of an episodic nature. It can be moved in time pretty easily. In outer space, as mentioned but recently the movie 'O Brother, Where Art Thou' put it in the depression era American south.
But I mentioned that I thought of one possible place where you could redo the Iliad fairly easily. Comic books. The personal battles are easy to create. Even in an enormous battle scene you can have Thor battle the Juggernaut, for instance. You can have two sympathetic sides fight against each other, say the X-Men and the Avengers. And the comic book universes have dabbled with higher powers that pull the strings, even to representing pantheons of myth. If someone wanted to do a modern retelling of the Iliad, this is the only route that came to my mind.