The 27-year-old moved from Lyon to Arsenal last summer and went on to score 14 goals in 32 appearances during his debut season in North London.
However, Lacazette started just four of the Gunners' final 12 Premier League outings last term, with Pierre-Emerick Aubameyang's January arrival putting the Frenchman's first-team spot under threat.
This season, Lacazette has found himself on the bench for all three of Arsenal's Premier League games, with new boss Unai Emery favouring Aubameyang as a lone frontman.
According to Le10Sport, the France international is now pushing for a move before the European transfer window closes at the end of the week.
The report also claims that several clubs on the continent have already made contact with Arsenal to ask about the player's availability before Friday's deadline.
However, the Gunners are reportedly desperate to hang on to Lacazette until January, with the Premier League transfer window already closed.
Arsenal are back in action on Sunday when they take on Cardiff City in South Wales.