Rooney's two goals in the 2-0 victory at West Ham United on Saturday took his tally in all competitions to 212, putting him third on the all-time list behind Charlton (249) and Denis Law (237).
"I have said before I have no problem with Wayne Rooney breaking my goalscoring record here and for England," Charlton told United's match programme for Tuesday's derby with Manchester City at Old Trafford.
"Not at all. Actually, I told him to do it as quickly as he could! He's a great striker and a great player - as hard as nails too.
"I've already said to him that I expect I'll be the one who has to present him with any award so he needs to make sure he does it!"
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