Could "in the aiport" be correct too?
In general probably yes, but how exactly do you want to phrase the sentence here?
Did he sleep in such airport?
Please see my rant in my other comment.
I think you need an article.
Did he sleep in an airport like this?
Who knows, maybe he did.
Or is this a suggested translation? Please use "My answer should be accepted" and if you also discuss here, tell us explicitly what you want us to do with the sentence.
According to my short research sleeping in an airport is indeeed possible.
I will add it in a few sentenced now, but someone more experienced may review or reverse that.