The Addicks boss told the club's offical website: "We've been talking to Sheffield Wednesday about Akpo. It's unfortunate for him because he did really well to play 90 minutes against Brentford and there was an opportunity for him to play two more games for us and himself, because he needs football.
"He hasn't played much over the last 12 months, but we're talking to Wednesday and we'll see if that progresses over the next few days."
Sodje, younger brother of Charlton defender Sam, has played nine times for the Addicks since arriving from Wednesday, who appointed Alan Irvine as their new manager earlier this week, in mid-November.
Mooney joined up with Parkinson's side in October and has made nine appearances, but has recently been nursing a knee injury.