Davis has been missing since being stretchered off with a knee injury early on in the 3-0 home defeat to Gillingham just over two weeks ago.
The 22-year-old could be back in training towards the end of this week, with one eye on next Tuesday's encounter against Stevenage at Gresty Road.
Alex boss Steve Davis told the club's official website: "We are hopeful Harry will come back into it soon. He has worked hard to get back and done well in his rehab work.
"He could be back with us towards the back end of this week but he will definitely be back for next week."
Meanwhile, striker Ryan Colclough has had an injection in his hip/groin in a bid to help him recover from the troublesome injury sustained in early September's 1-0 Johnstone's Paint Trophy victory over Accrington.
Steve Davis added: "Ryan has had an injection to help with the discomfort and soreness he has been suffering with and we will have to see how that settles down."