Left-back Bertrand was removed before half-time of Saturday's 3-1 defeat at West Brom after taking a knock to the head while Mills has a shin injury.
Rodgers said: "Ryan didn't know where he was so I had to take him off while Mills will be assessed after getting a whack on the shin."
Darren O'Dea and Alex Pearce could come into the side but full-back Chris Armstrong remains sidelined with his knee problem.
Striker Simon Church missed out at The Hawthorns after collecting an injury while on international duty with Wales but Shane Long did return from a niggle and could start if required.
