The 21-year-old defender has been a regular for the Italian outfit during the 2020-21 campaign, clocking up 28 appearances in all competitions, including 20 in Serie A.
The Italy international only has little more than two years remaining on his contract at San Siro, though, and according to Calciomercato, the Catalan giants are keen on bringing the centre-back to Camp Nou.
The report adds that Barca want to freshen their defence ahead of the new season, but Nerazzurri are believed to value Bastoni somewhere in the region of £52m.
Due to the financial concerns arising from the coronavirus pandemic, it could be difficult for the Spanish outfit to find the required funds in the upcoming market.
Bastoni racked up 61 appearances for Inter since his move from Atalanta BC in 2017.