Rooney netted his 202nd goal for the Reds on Saturday as they suffered a 2-1 defeat at home to West Bromwich Albion in the Premier League.
The 27-year-old is now just 47 goals behind Charlton's record tally of 249 for United.
"I've spoken to Wayne and I've told him he's doing really, really well. Fantastically well," the 75-year-old told the club's official website.
"I'll lose no sleep over it at all if Wayne beats my record. It will be something else for the club to be proud of. And he can buy the drinks!"
United return to action on Wednesday when they travel to Ukraine to face Shakhtar Donetsk in the Champions League.