Davies, who stepped up from the youth team to take over from Bobby Williamson in the spring, was dismissed after the Blues' FA Cup first round defeat at home to Millwall.
The move leaves the club in turmoil once more, having had 12 changes of manager since 2000. Stephen Vaughan is expected to offer the caretaker manager role to Davies' assistant Wayne Allison today.
Davies' record this season has seen his side concede 41 goals in league and cup and register just three wins in League Two. In the frame should Allison turn down the offer are former Wrexham boss Brian Little, former Notts County boss Steve Thompson and Steve Bleasdale, who was Mark Wright's assistant when Chester won the Nationwide Conference and who is reported to have attended the Millwall game.