The defensive duo are both finalising moves to The Valley after becoming surplus to requirements at their respective clubs.
"There's creeping movement on that one, I would say," Royals boss Steve Coppell told the club's official website regarding Sodje. "Inevitably there will be a last minute flurry of activity.
"Something will happen I think, but it might be a loan, not permanent."
In addition to Sodje, Charlton are also near to agreeing a deal to bring Manchester City full-back Mills back to the club.
Mills has been told he can leave City by his former England coach Sven Goran Eriksson and is set to link up with The Addicks until January.