Defender Davies is struggling with a back problem and Reid has suffered a slight recurrence of the groin injury that kept him out at the back end of last year.
"They're both not serious injuries," said manager Phil Parkinson. "Whether Tuesday comes too soon for them we'll have to wait and see."
"Andrew's is not a muscle problem, it's more coming from his back.
"It's not something we're overly concerned with, but it's something which has flared up a few times of late and he felt it in Saturday's warm-up.
"Kyle's groin tightened up. Nothing like the injury he got before Christmas. We'll monitor that, but I don't think it's too serious."
If they miss out Michael Nelson is likely to continue at the heart of defence and Will Atkinson in a wide midfield role.
Parkinson has no other new injury worries as his side look to open up a four-point gap between themselves and eighth-placed Exeter.