The youngster has been dubbed the new Marco Verratti for his style.
The 17-year-old is a top prospect in his age group, and Sportsuggests that Barca are very keen to sign him.
Michut has been with PSG since he was 13, but would be willing to move if he has a better chance at first team football elsewhere.
He has played for France's under-16s and 17s as well.
Any move would be complicated given he is not yet 18, but both Barca and City are hoping to make something happen this summer.