The only sane intepretation of this is wife. It lines up perfectly with the 10th commandment. Additionally, as polygamy was still common then, it most certainly was not against married men.
Not saying it is fair, but Jesus clearly was talking about adultry, which means only a taken women. Men could have many wives, but women could not have more than one husband.
I don’t consider the Bible authoritative on this though, as these rules were what society was at the time. Today, adultry would me a married man or women. If both were ok with it, in the sense of swingers, then it would no longer be adultry.
If you notice, the word desire/covet doesn’t limit itself to a sexual context. If someone else’s wife cooks a great meal and you desire that trait, it would be no different than desiring her beauty, which is another trait. But the term covet is stronger, and conveys the idea of trying to obtain the person, effectively stealing another’s property (as it would have been in those days).
You are stealing nothing to admire another’s traits. But if you are seeking to obtain those for yourself, then your heart is geared towards the deed, should it arise, and this is the beginning of the seed of sin, not before.
I like Gary’s A’s thing about “reading the white”, too many people study so the word so intently that they miss the big picture. This causes us to obsess over the words vs the heart of the matter, and, of course trying to label normal and healthy desires as evil is a recipe for disaster and slavery.