The Spanish champions are believed to have identified Martinez as their leading target in this summer’s transfer window, with the club thought to be keen to secure a long-term Luis Suarez replacement.
The 22-year-old has a €111m (£99.7m) release clause in his contract at San Siro, but Barca are thought to be keen to offer at least one player as a makeweight in order to lower the price.
According to Calciomercato, Inter want €85m (£76.3m) plus Junior Firpo in exchange for Martinez, but the Catalan giants are only willing to spend €65m (£58.4m) in cash, in addition to one or two first-team players.
The South American has scored 16 times in 32 appearances for Antonio Conte‘s side this season, including five goals in six Champions League outings.
The forward’s current deal with his Italian club is due to run until the summer of 2023.