The 22-year-old winger has impressed during a one-month loan spell, scoring against Gillingham and tearing several more teams to shreds with some mazy dribbling.
Royals boss Alan Pardew revealed that he is attempting to keep Chadwick at the Mad Stad.
"Sir Alex Ferguson has been difficult to get hold of with Champions League and Worthington Cup commitments, but I hope to pin him down this week and extend Luke's loan," he said.
Chadwick, who has struggled to break into the Man Utd team this season, is scheduled to return to Old Trafford on March 15th, following Reading's game with Crystal Palace.
With the Cambridge-born man in the side the Royals have gone on an unbeaten run which saw them rise as high as third in the league prior to their defeat at the hands of Wimbledon on Saturday.
If Pardew was to keep Chadwick with his Berkshire side it would be seen as a major boost to the Royals push for promotion to the Premiership.