Balogun, 19, looks to be a major star of the future after making his first-team breakthrough this season.
However, his contract at Emirates Stadium expires this summer and Arsenal have held talks over an extension.
But an agreement is yet to be reached - and according to the Daily Star Sunday Liverpool are lurking.
They state, via The Athletic, that Jurgen Klopp's side are huge admirers of the player and with talks failing to result in an agreement, they claim his exit from North London is looking increasingly likely.
That could see Balogun make a free transfer switch to Anfield in the summer. However, the report states there is also overseas interest in the striker from the Bundesliga.
Indeed, Arsenal are growing increasingly worried as Balogun can negotiate with interested foreign suitors from January 1.
Mikel Arteta remains hopeful Arsenal could yet convince Balogun to sign a new deal.
After a 4-2 win over Dundalk in the Europa League, Balogun scored one and set up another.
Arteta said: "We are having some discussions with the player.
"He knows we want to retain him at the club. We know the length of his contract at the moment is an issue but we are trying to resolve it in the best possible way.
"We want him to stay and he told me he wants to stay at the club. Hopefully we can reach an agreement and extend his contract."
Balogun has featured heavily for Arsenal's U23s this term, scoring four goals and notching two assists in Premier League 2.
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