Charlton scored 249 goals for the Red Devils and 49 times in 106 matches for England during his career.
"It's a great challenge," The Mirror quotes Rooney as saying. "Sir Bobby is a legend and is such a presence around the club.
"If I could break his record as Manchester United's top goalscorer and maybe even England's... wow! That is such a great incentive."
Rooney has scored 184 goals for United and has found the target 32 times for England so far.