Aneke has impressed during three months with the Railwaymen and he came off the bench to complete the scoring in last Tuesday's 4-1 Johnstone's Paint Trophy triumph over Bradford - the 19-year-old's sixth goal in 22 appearances.
"Chuks' loan agreement is up and we will speak with Chuks and Arsenal to see what their feelings are on it," Alex boss Steve Davis told his club's official website.
"Chuks has been here for three months, away from London and his family and friends, so we will see how he feels at staying on.
"He is a young and talented lad. He has got great ability and will only get better with experience. He can create and score goals and I think he has gained a lot from the experience. He has settled in well and is popular with the lads and around the club.
"He has his weaknesses as well. He knows he has to be better when we are not in possession. We have spoke about him being more of a team player and helping defensively.
"He played really well against Bradford. He came on and changed the game. He has scored six goals and is our second leading scorer, so we have been pleased with his impact."