For things that are merely impossible, the answer is yes. Though the answer is no if talking about things which are also inconceivable.
It is almost obvious that we can want impossible things in the sense of wanting things that science says are impossible.
While there remains room for theories to change, our present understanding of physics suggests that it is impossible for ordinary matter, much less living humans, to travel faster than light. But lots of people want there to be a way to safely travel faster than light for practical reasons.
True immortality in this universe is almost certainly impossible for humans. There are reasons to believe it is biologically impossible to stop the aging process completely and even if we somehow overcame that, entropy shows that life as we know it must eventually stop. Yet you will find no shortage of people seeking for immortality.
Now, if we talk about things which are truly inconceivable, then it is impossible to want them, at least in a meaningful way. But the reason for that is that things which are both impossible and truly inconceivable are, at least when examined, essentially meaningless gibberish so to say that you want them would remain meaningless gibberish.
The quintessential example of something that would fit into this category is a "round square", but a round square is conceptually impossible to the point of being essentially gibberish. A direct contradiction inside the term itself which makes it so it could have no meaning. It would be equally meaningless to say that I want a round square.