The Catalan giants are said to be on the verge of agreeing a deal for Eric Garcia, who is leaving Manchester City on a free transfer this summer, but Ronald Koeman's side are allegedly still looking for another centre-back.
According to Mundo Deportivo, Bastoni is being considered by the Catalan giants, who have been impressed by the 22-year-old's performances during the 2020-21 campaign.
The Italy international has provided four assists in 39 appearances for Antonio Conte's side this term, while he played a key role in his team securing the Serie A title.
Bastoni only has little over two years left to run on his deal at San Siro, though, meaning that his long-term future with the Milan giants is unclear.
Inter are believed to value the centre-back in the region of £52m, which Barca are unlikely to be able to afford in the upcoming market as they deal with the financial implications of the coronavirus outbreak.