The Gabon international impressed at the Emirates Stadium following his arrival from Borussia Dortmund in January, scoring 10 goals in 13 appearances.
Kanu, who played for Arsenal between 1999 and 2004, is hoping that Aubameyang can press on in his first full season and spearhead the team in their pursuit of the championship.
"If he can perform, if it's a good season for him they have a chance to win the league," the 42-year-old told Sky Sports News.
"Aubameyang's very, very good. Last season was his first season; now he has adjusted to the Premier League. He's been playing well with the new coach and his teammates; this season is going to be his season, if he works for it."
Arsenal, who will be managed by former Sevilla and Paris Saint-Germain boss Unai Emery this season, have not won the title since 2004.