Arsenal forward Aneke is spending his second season on loan at Gresty Road and has already found the net 10 times, including a brace in Saturday's 3-0 win over Sheffield United, to add to the eight he managed last term.
The 20-year-old sees his Gunners contract expire at the end of this season and, should fresh terms not be on offer at the Emirates Stadium, then he faces a decision over his future.
Davis told Crewe's official website: "Signing Chuks on a permanent basis is something I've thought about but it is maybe a bit early for him to decide what he is going to do in the summer.
"His agent was very keen for him to be here and everyone can see the improvement he has made when making that step up from Under-21 football.
"We won't be able to compete with a lot of clubs financially but Chuks has to fit into a style of football, if I was going to give him any advice it would be that the team he plays in is very important to him because of the style of player he is.
"I think we are one of very few clubs who could accommodate him at this level, and I have been very patient with him."