Hargreaves told the BBC: "The thing is, Cristiano can do even better, he can do more, and I think he will.
"He just wants to be the best, and you can see that in him. There's no doubt for me that he will get there, if he's not there now."
Ronaldo is fast closing in on Old Trafford legend George Best's record for goals scored in one season by a non-striker for Manchester United.
That mark stands at 32, and Hargreaves has no doubts that the goals will keep coming for his 22-year-old fellow midfielder.
The England international said: "I think he's got to the point now where you'd almost be surprised if he didn't score, he's in such good form.
"Cristiano works very hard, has got great discipline, and it's great to see him playing so consistently."
