The Athletic says negotiations between Arsenal and Sevilla are running in parallel with talks over a new deal with Thomas Partey.
Agoume is viewed at Arsenal as a replacement for Partey, whose deal expires at the end of June.
The 23-year-old came off an impressive last season with Sevilla and is a former Inter Milan prospect.
While Martin Zubimendi is due to arrive from Real Sociedad, Arsenal remain keen to add another midfield signing, and Agoume is emerging as their prime target.