Aneke is currently suspended for three games after being sent off last weekend.
"We are now without Chuks for three games and it is disappointing because we are short of midfield players," Davis told Crewe's official website. "It is also disappointing for Chuks because he wanted to come here and show everyone the ability he has.
"He wants to play and we will discuss about extending his loan or not when the time comes. We haven't made a decision yet and I will contact (assistant manager) Steve Bould at Arsenal and discuss things. He would have seen the challenge and know that he isn't that sort of player.
"Chuks has ability and it is a shame that he hasn't been able to have the impact he would have wanted because of his three-match suspension."