Konchesky has joined the Reds on loan from Liverpool and is expected to make his debut at left-back.
With the short trip to the Ricoh Arena coming little over 48 hours after the FA Cup defeat at West Ham, Davies will shuffle his pack.
The Scot made four changes at Upton Park on Sunday. Marcus Tudgay, cup-tied against the Hammers, should come back into the team, with fellow forwards Robert Earnshaw, Nathan Tyson and midfielder Guy Moussi also in line for recalls.
Midfielder Paul Anderson is still a doubt with the hamstring problem that has ruled him out of the last two matches.