The Italy Under-21 international is regarded as one of the emerging prospects in Serie A, with 73 appearances having already been made for his current club.
That has resulted in widespread interest in the 21-year-old's signature, with Liverpool said to be monitoring the situation ahead of a future approach.
Juventus were said to be among a number of Italian sides keen on Barella, but according to Calciomercato, the top-flight champions are not planning to make a move in the near future.
Massimiliano Allegri's squad is currently well-stocked with midfield players, and it has been claimed that Juventus are not keen on making another major addition in that area of the pitch.
Barella still has just under four years remaining on his contract.