The landmark goal took him past Charlton's tally of 249 with Rooney managing the feat in 212 games less.
The 31-year-old came off the bench in the draw with Stoke, a role he has become familiar with under Jose Mourinho this season.
Wayne Rooney became Manchester United's all-time leading goalscorer against Stoke
Wayne Rooney began his career at Everton
The England captain has struggled to hold down a regular place in the first team under Mourinho with Rooney starting just eight Premier League matches.
And Redknapp believes Rooney has nothing left to prove at United and should end his career at his boyhood club.
"Mourinho doesn’t see him as a starter," Redknapp told talkSPORT. "He doesn’t think he is better than Zlatan.
Wayne Rooney's record-breaking goal in pictures
Sun, January 22, 2017
Click through the gallery for the best snaps of Wayne Rooney's landmark goal
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Click through the gallery for the best snaps of Wayne Rooney's record-breaking goal for Manchester United
Harry Redknapp wants Wayne Rooney to return to Everton
"Maybe it is time for him to have one more challenge – go somewhere where he is wanted and going to be a big player.
"He could go back to his old club Everton. He is an Everton fan. Go back there, finish your career there and take Everton into the Champions League positions.
"He could go there and turn them into a top four club. He could make the difference.
"He could help these young kids who have come in. Imagine having Rooney back around to help on the park, look after them and teach them the game."