Cagliari midfielder Barella has been on the radar of fellow Serie A sides Juventus, Inter Milan, AC Milan and Roma, though Liverpool have now jumped to the front of the queue to bring in the player.
The 21-year-old opted to stay at boyhood club despite interest from top teams this summer.
Barella said: "The transfer market? I feel at home with the team of my city.
"Together with the president, I decided to prolong my relationship with them, rejecting the offers that came my way.
"I didn't even take them into consideration. My first choice has always been Cagliari.
Barella has also earned a place in Roberto Mancini's Italy squad in recent weeks, though is yet to make his debut for the national side.