Wizards don't have a 1st Rounder this year. It was given up in the Gortat trade. I think they would only be interested in Green if they can't retain Ariza.
I would think they could easily fit both Ariza and Green in the rotation. I mean you are talking about a team that started Trevor Booker and Martell Webster a combined 58 games. I would think Jeff Green makes more sense to start than either of those guys and could see giving him 35 minutes at the 3 and 4 (and maybe a bit at the 2 if they want to go big).
As for a trade, I just don't see any team giving up a whole lot of value for Jeff Green and they have no expiring contracts except for Andre Miller to trade, so I don't see any real way to get that done unless they are willing to give up on Otto Porter and then include Miller, which I just don't see as happening.
EDIT: If the Wiz would trade Miller and Porter for Green, I think it might make some sense, especially if Boston can find a third team to take Miller and get something different back (maybe Miller & Bogans to NY, Green to Wash, and Porter and Bargnani to Boston - or something like that).