"grow fascinated" is a correct phrase and can be used in written English.
It means to become increasingly captivated or interested in something. You can use it when describing a gradual change in someone's feelings or emotions towards a particular subject. Example: As she spent more time studying the delicate petals of the flower, she began to grow fascinated by its beauty and intricate details.
He grew fascinated by advanced technologies and, more important, the kind of society that advances them.
While attempting to modify this classification, I grew fascinated by Strachey's work.
I was growing fascinated by the numbers so I asked how many of these books they published each year.
Discontent with standard Western conceptions of tuning and intonation, Partch grew fascinated with alternative approaches, especially Asian systems.
Kochan grew fascinated - some say obsessed - with the implications of the second commandment, the stricture on idolatry.
Saki was my own initial thought, the Saki of the waggishly precious, or semi-precious, observation ("She grew fascinated by the curtains, which were doing nothing in particular").
While making Architecting, performer Kristen Sieh became obsessed with Teddy Roosevelt, while King grew fascinated by Elvis impersonators while researching Mission Drift in Vegas.
I've been watching "Queen Sugar" since it premièred, last year, and have grown fascinated with its soapy yet increasingly thoughtful and provocative story lines.
The student and Mr. Cho were in another class as well, a small class on playwriting, during which she grew fascinated by him.
In recent years, for example, menswear enthusiasts have grown fascinated by Italian style; men like the late Gianni Agnelli, who was president of Fiat and the richest man in Italy, have become style icons.
As I entered people's homes and offices, penetrated their personal spaces, I grew fascinated with the walls as anthropological records, a way to capture the essence of people without having them in the picture.
