The two clubs are yet to finalise the exact structure of an agreement, but sources have indicated the Ligue 1 side are now in pole position to sign the 22-year-old amid interest from Inter Milan and Chelsea.
Both Inter and Chelsea were put off by Arsenal's original €58.3m asking price. Arsenal's willingness to compromise could force a rethink but sources have suggested that Chelsea's valuation of the United States international was much lower.
Given the significant difference in their valuation of the player, Chelsea had not followed up an enquiry with a formal bid as of Friday morning.
Balogun has not been involved in either of Arsenal's Premier League matchday squads this season and is seeking regular first-team football after an impressive loan spell at Reims where he scored 21 goals in 37 Ligue 1 games.
Arsenal are seeking to offload several fringe players with Kieran Tierney close to joining Real Sociedad on a season-long loan while Nuno Tavares, Cedric Soares, Nicolas Pépé and Albert Sambi Lokonga are among several others made available before the Sept. 1 deadline.