"construct a story" is correct and usable in written English.
You can use it when you want to ask someone to write a narrative or short story. For example, "Please construct a story about a magical creature that lives in a forest."
Unlike Ella, I could not construct a story that would help me comprehend what was happening.
"I think you can construct a story linking the pressure for financial performance to those ethical breaches.
Mr. Wasik sees himself as a brand architect, "somebody who can see pieces and construct a story that makes sense.
A reason the humanities are so vital to science is that it takes a great imagination to construct a story.
He was resolved to construct a story that was both credible and fantastic but had no cracks.
But if good people are considered ineffectual to begin with, or, even worse, a nuisance or irrelevant, then it's virtually impossible to construct a story around their efforts.
How do you go about constructing a story such that the ending reveals something about the beginning?
Using these events as a narrative armature, Mr. Harbach skillfully constructs a story with startling depth of field.
Students said they struggled with questions that asked them to discuss how a writer constructed a story rather than about the content of the passage itself.
"There is a radical error, I think, in the usual mode of constructing a story," Poe writes in "The Philosophy of Composition," a great, mad essay from which young scribblers may still profit.
Ditching the aloof irony of his earliest works, he constructs a story that is funny, incisive, profanity-laced and illuminating -- full of difficult-to-like underdogs whose vindication and enrichment we end up cheering.
