Sao Paulo are reportedly not fearful of losing Brenner despite the widespread interest in his services.
The 20-year-old has scored 19 times in 39 appearances for his Brazilian side, and a number of clubs are believed to be closely monitoring his performances.
However, according to Globo Esporte, Sao Paulo are not prepared to sell the Brazilian for anything under his €50m (£44.5m) release clause.
As a result, the report claims that the Gunners are expected to be priced out of a move as they are not prepared to pay that amount for the youngster.
Brenner has scored 17 times in 27 appearances at club level during the current season.