The north London side reportedly isn't planning to offer him a new deal before his contract expires next summer, according to Matt Hughes of The Times.
That means the 28-year-old can sign a pre-contract with another team as soon as January.
The England international is dealing with a serious knee injury that required two surgeries. It's unclear if he will return this season, as Arsenal have not provided a timetable.
Welbeck is the latest high-profile Arsenal player who appears destined to leave on a free transfer following reports that the Gunners decided against extending Aaron Ramsey's stay. The Welsh midfielder said earlier this season that he was close to signing a new deal before Arsenal withdrew their contract offer.
Welbeck's made 126 appearances for the Gunners since joining Arsenal from Manchester United in 2014.