The Blaugrana are reported to have had scouts monitor the progress of the 20-year-old playmaker after he rose to prominence with a hat-trick in the final of the 2011 FIFA Under-20 World Cup in the summer.
Milan have been linked with the player, whose full name is Oscar dos Santos Emboaba Junior, for several weeks but have yet to make official contact, according to Sport.
Internacional have seen scouts from several major European clubs attend their games due to the interest in striker Leandro Damiao and reports soon filtered back about Oscar.
Tottenham have a partnership agreement with the Porto Algre-based outfit and could have first refusal on the youngster if they want to make their interest concrete.
Oscar joined Internacional from Sao Paulo in 2010 and has made only 22 appearances for the first team after playing only as handful of times before making the move.
After helping his club win the Copa Libertadores in 2010, the midfielder won the Campeonato Gaucho and Recopa Sudamerica this year.
Last month Oscar made his first two appearances for Brazil's first team when he played in the Superclasico de las Americas double header against Argentina.