Alex achieved a creditable 13th place on their first season back in League One and also picked up the Johnstone's Paint Trophy with a 2-0 Wembley victory over Southend last month.
"I am happy with the squad I have but I would like to add at least three quality players if I can," Davis told his club's official website. "I think we are okay for goalkeepers and defenders.
"We may have to strengthen in midfield, depending on what might or might not happen there. I would like to attract another ball player and that doesn't have to be an experienced one. It could be a younger one with potential.
"I also want some pace from the wing and a target man. Mathias Pogba could be that one but I think you need that type of target man to try and get out of the division. It would just give us an extra option up there."
Davis' desire for an experienced target man has prompted speculation that Rob Hulse could make a return to Gresty Road when the 33-year-old's deal expires at QPR during the close season.
"He's the type who would help us, I know him and he's a local lad," Davis told BBC Radio Stoke. "He might be an option, who knows?
"I've not spoken to him, so I don't know what his contract situation is.
"He's not a young lad anymore and his career has been drifting around over the last two or three years but he knows the league, he's been in the Championship for a long time and he has that experience that would help the younger players."