Balogun scored 10 goals in 15 games for the club’s under-23s during the campaign, but he is yet to make his debut for the senior team despite regularly training with them.
The England youth international signed his first professional deal in February 2019, but it expires at the end of next season and Arsenal aren’t ready to lose him for free.
They knocked back a £5 million offer for Balogun from Brentford in January, and Southampton will have to table a better bid if they want him.
Arsenal are also expected to include a sell-on clause in any deal, and that shouldn’t be a problem for the Saints.
Ralph Hasenhuttl’s side finished the Premier League campaign in 11th place and will look to break into the top-six next term.
Strengthening the attack will help boost their chances, and if Balogun can replicate his goal-scoring heroics at youth level on the biggest stage if he moves to the south coast, Southampton could end up with a real gem.