The 19-year-old, who is the son of former Italy international Enrico Chiesa, has burst onto the scene at Fiorentina.
Despite being a teenager, the winger has established himself in the first team and he has caught the eye with some of his performances.
Liverpool, according to Calciomercato, have taken note and they are now said to be tracking Chiesa ahead of the January transfer window.
Plenty of other clubs are also watching the Italy under-21 international, though, including AC Milan and Inter Milan.
Fiorentina, however, have no plans to part with Chiesa and see him as a big part of their future going forward.