The 21-year-old has returned to the Gunners after spending the second half of last season on loan at Middlesbrough.
Despite beginning pre-season with Arsenal, the summer signings of Gabriel Jesus and Fabio Vieira could hinder Balogun's playing time.
With Balogun believed to be low down the pecking order at Arsenal, a summer departure looks to be on the cards, with Reims emerging as a potential destination.
According to The Sun, Reims have identified Balogun as a potential replacement for Hugo Ekitike, who has left the club to join French champions Paris Saint-Germain.
Reims are not looking to pay above the odds for the Arsenal striker, which could prove problematic with three years still left to run on Balogun's current contract.
The Arsenal academy graduate is reportedly on a three-man shortlist, with Reims also considering Genoa's Aleksander Buksa and Genk's Junya Ito as Ekitike's replacement.