Even though Alex is currently "with" Lexie, his heart's clearly still with Izzie. Now here's the question: will he ever get closure.. and more importantly, will we?! Well we've got spoilers that'll answer this question so check them out!
Never fear! It seems that Grey's showrunners are just as concerned with getting closure as it relates to Alex & Izzie as we are. Showrunner Rhimes says that Alex finding closure is one of the top priorities for this season. She says that she, as well as the other Grey's writers, are "talking about it [in the writers' room] obsessively and trying to figure it out. We’re approaching it pretty carefully."
We can expect the following next season for Alex: "Alex growing up and moving on and moving past that relationship." The writers are working hard to make sure that all of this is handled delicately and in a way that's authentic.
Also, a little tidbit that's interesting: Rhimes says that Alex's story will not take "the expected form." As for whether or not Katherine Heigl will be back as Izzie, Rhimes had a noncommittal "I don't know" to say.
Source: Ausiello Files