The Gunners regard Aneke as an exciting prospect for the future but first-team opportunities may be hard to come by due to the abundance of midfield talent at the club.
It is understood that Arsenal will therefore not stand in the way of the 20-year-old moving on this summer, with his contract due to expire at the end of June.
Aneke has enhanced his reputation during loan spells with Crewe Alexandra over the past couple of years, having previously gained experience on loan at Stevenage and Preston North End at the start of his career.
The former England U16, U17 and U19 international could now be set for a free transfer as it is understood that he is attracting considerable interest.
Fulham, Charlton Athletic and Millwall are all believed to be keen on Aneke.