The 27-year-old Nigerian defender would have been a useful addition as Dennis Wise looks to strengthen a back four that has conceded 30 goals in 15 games in the Championship so far this season.
Sodje, who joined the Royals from Brentford for £350k in the summer, has played in only two games so far this season for the Premiership side.
But after already losing on-loan defender Peter Mate for the rest of the campaign to a serious knee injury, manager Steve Coppell is concerned at a lack of cover if he lets Sodje join United.