The Brazilian attacker – who is comfortable on either flank or in a ‘number 10’ role – emerged as one of the hottest talents in European football last term as he notched 16 goals and registered 11 assists in the German top tier.
His displays have attracted attention from big sides across the continent, with Liverpool thought to be one of the teams at the forefront of the queue for his signature.
But Arsenal are now ready to edge ahead of their rivals with an £8m offer for the 22-year-old.
Although Arsene Wenger already possesses a wealth of talented attacking midfielders, the Frenchman is believed to see Firmino – who can operate as a striker – as a good option as he looks about building a squad capable of a sustained title push.
Inter Milan are also thought to be serious about getting the South American on board, while Chelsea were linked with him in January.