Bell, who has been out since mid-January, is now able to kick a ball again and Davis has welcomed the midfielder's desire to return.
"Lee is progressing really well at the moment. He has his own programme and we will monitor him to make sure he is fully right when he comes back," Davis told the club's official website.
"It won't be long with him because he is determined to get back as quickly as he can. He, as is usual with Belly, has shown a great attitude."
Fellow injury-hit defender David Artell is receiving treatment for a hamstring injury, but is suspended for the weekend clash with Port Vale.
Crewe last week