Mikel Arteta has made the striker available for transfer this summer, as he seeks to raise funds for more reinforcements - mainly in midfield and at right-back.
Balogun spent last season on loan at Reims, where 22 goals in 39 games has put him on the radar of leading European clubs.
Arteta has given the decision considerable thought, given that Balogun could be a hugely useful option for Arsenal.
But the manager is willing to let him go both to raise funds and for the benefit of the 22-year-old’s career.
Arsenal are attempting to raise up to £70m on sales of players such as Kieran Tierney and Balogun, with the club linked with moves for Mohammed Kudus and Romeo Lavia.