Former Everton starlet Green, who joined Chester last week from fellow National League North side Nuneaton Borough, had been named on the bench on Saturday for the clash with the Shakers but was advised to sit the game out after feeling a twinge in his lower back.
The 22-year-old attacking midfielder was advised a couple of days rest and may come into contention for this evening's clash with League Two side Morecambe at the Swansway Chester Stadium (7.45pm).
Chester joint-manager Bernard Morley said after Saturday's game: "It's just irritating (him) and when it flares up it's not going to go away. The physio said you just need to give it another 48 hours and take it from there."
One player who is likely to return is winger Craig Mahon.
Mahon, Chester's longest serving player, missed the Bury game owing to him attending his sister's wedding in Ireland.
And Morley and co-boss Anthony Johnson are set to run the rule once again over a trialist striker from a League One side who appeared as a second-half substitute against Bury on Saturday, as well as former Oldham Athletic striker Deane Smalley, who has been on trial with the club since the start of pre-season.
Morley added: "We have got to be looking at Morecambe and thinking that is where we are trying to aspire to. Do we expect to get beat? Not at all. We expect to match them and expect to get more shots on target (than they did against Bury). That will be the message to the lads.
"I'm looking forward to it. I'm hoping to see a little bit more improvement."