The 21-year-old has been sent on loan to Birmingham, Walsall and Charlton since arriving at the club in January 2015.
Bielik hoped to be rewarded for his patience with a first-team squad place ahead the 2019/20 campaign but the Evening Standard reports that he is not in boss Unai Emery’s plans.
The Gunners hierarchy would like the Poland Under-21 international to sign a new contract before heading back out on loan.
But interest from Milan could be difficult for the 21-year-old to resist despite Arsenal’s reluctance to sell the player.
Bielik made 31 appearances for Charlton last season as they earned promotion from League One and he currently has a deal until 2021 with the Premier League side.
He impressed during the recent European Under-21 Championship, scoring two goals in three games during the group stage – including the winner against hosts Italy.
The report adds that the Pole’s path to the first team in north London will be further complicated if Arsenal make a concerted push to complete the signing of Southampton’s Mario Lemina.
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