The London club would want around £45m for the 22-year-old, although there is still some distance to go on price.
Balogun is also wanted by Internazionale, AC Milan, Roma and Olympique Marseille and it would usually have been thought that Chelsea would offer the most enticing option, given they are in the Premier League.
With the US international having last season enjoyed a loan at Reims, however, his own preference is to stay abroad – particularly in Ligue Un.
Internazionale had previously been seen as likeliest to sign the forward, but could not get close on price.
Chelsea have also been put off by Arsenal’s asking price, although they are now actively searching for a number-nine, which is proving an increasingly difficult market.
Price is an issue that may yet see a late twist in any deal, but Monaco are so far closest to what Arsenal want and most advanced in negotiations with the club.