It had been feared Ronaldo would be missing for at least three months after an operation on his right ankle in Amsterdam on July 7.
Ronaldo, 23, said: "I am feeling fine. I am feeling really good and my recovery is going well.
"I am more than happy with my progress and I hope to be back playing for United by the end of September - that is my target and it is a realistic one.
"It has been frustrating to miss the start of the Premier League season but I am pleased with my rehabilitation and, hopefully, I'll be ready soon."