The 24-year-old has been in impressive form for the Italian champions at the start of the 2021-22 campaign, scoring once and providing five assists in seven Serie A appearances.
Barella still has three years left to run on his current deal, but there was speculation surrounding his future during the summer transfer window.
According to Gazzetta dello Sport, Liverpool have recently approached Inter to discuss a possible move for the Italy international next year.
The report claims that Paris Saint-Germain are also interested, but Inter are becoming increasingly confident of agreeing a new deal with the midfielder in the near future.
Barella has scored eight times and registered 26 assists in 96 appearances for his current club since making the move from Cagliari, initially on loan.