The 22-year-old has two years left on his Gunners deal, but hasn't featured in his club's campaign so far since returning from a season-long loan with Reims.
But the United States international has now been sounded out by Chelsea.
talkSPORT brought you the news that the Blues had held tentative talks with the striker's advisers.
Now, according to the Evening Standard, Arsenal are aware of the Blues interest and want around £50million for their star.
Balogun is open to the move, too.
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He netted 21 league goals in 37 matches in France last season, leading Fulham and Monaco to be interested in him.
Meanwhile, Chelsea struggled up front in their 3-1 defeat to West Ham on Sunday, despite the Hammers going down to 10 men.
Mason Burstow, a 20-year-old who signed from Charlton in January 2022 and spent last season in the Under-21s, came off the bench in the game, showing the Blues are in real need of some more experienced reinforcements.
This has been worsened by Sunday's goalscorer Carney Chukwuemeka's injury.
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Balogun is one of four forwards Chelsea are looking at, with the others being Nottingham Forest's Brennan Johnson, Ajax's Mohammed Kudus and Lyon winger Bradley Barcola.