Bacca has scored six goals for the Serie A giants so far this season.
However, despite his form, the striker has fallen out with manager Vincenzo Montella.
The Colombia international missed the club's win over Empoli last weekend - but angered Montella by training with former club Sevilla.
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Arsenal are keen on a move for Carlos Bacca
GETTY
Carlos Bacca nearly joined Arsenal during his time at Sevilla
And The Sun on Sunday claim that Arsenal have opened talks over a January transfer.
The Gunners have been hit by a traditional injury crisis with three strikers currently out.
Olivier Giroud missed yesterday's 5-1 win over West Ham with a groin injury while Lucas Perez and Danny Welbeck are also sidelined.
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Danny Welbeck is one of three Arsenal players out injured
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Arsenal boss Arsene Wenger is said to be determined to sign a striker in order to keep their hopes of winning the Premier League alive.
Wenger previously tried to sign Bacca during the striker's time in Seville, only to lose out to Milan instead.
But that has not deterred the Frenchman from trying again and - despite Alexis Sanchez's fine form - wants to add more firepower to his squad next month.
Bacca was a target for West Ham in the summer but ultimately opted to stay at the San Siro.