The 22-year-old suffered medial ligament damage to his knee in last week's 2-0 defeat to a Manchester United XI.
"It's not good news concerning Mathias. He has a medial knee ligament injury and it will be months rather than weeks with him," Davis told the club's official website.
"We'll see how he is once the bruising settles down, but it doesn't look good. It was a bad challenge because the full-back has left the ground and followed through.
"Pogs should have avoided being involved in the tackle, but he went into it and it was risky. It's difficult to put an exact time span on it, but it will be a month or two."
Pogba suffered the injury in a clash with United defender Scott Wootton.