The 26-year-old has been training with the Red Devils in pre-season following his excursions with England at Euro 2012 in June.
"I'm happy with how I'm doing," said Rooney. "I've been training for almost two weeks and I've been working hard. Everything's going well so far. I feel good.
"Everybody needs games to get up to match fitness, not just me. I'm training well, though, and I'm looking forward to the next few games. Hopefully, by the start of the season, I'll be ready to play."
United, who go up against Barcelona in a pre-season friendly this week, will face Everton in their first match of the new campaign on August 20.