The striker returned to Arsenal following a successful season-long loan at French club Reims, netting 21 goals.
But Balogun's exploits across the Channel has only increased his desire for more game time and he may have to leave the Emirates Stadium to find it.
According to Football Transfers, Balogun's representatives have touched base with Chelsea over a switch to west London.
The Blues now appear to be leading the chase for the United States international who has attracted attention from a host of European clubs.
AC Milan and Inter along with Marseille, Monaco and RB Leipzig are all tracking the 22-year-old following his breakout season in Ligue 1.
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Meanwhile, Chelsea are on the lookout for a No.9 despite the signing of Christopher Nkunku.
Kai Havertz's move to Arsenal has left Chelsea in short supply with Pierre-Emerick Aubameyang is likely to move on this summer after a disappointing spell at Stamford Bridge.
Balogun's path to first-team football at Arsenal is likely to be blocked by striker Gabriel Jesus and recently revealed he has no intention of securing another loan move.
He said: "What I can say is that I definitely won't go on loan again.
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"I'm not sure on the discussions that are going to take place, I'm not sure what's going to happen.
"But I'm just committed to now, I try to stay present."
The Gunners are unlikely to stand in Balogun's way if an offer matching their valuation is received.
Arsenal are thought to want £50million for their academy star ahead of a potential bidding war for the striker.