The England defender has yet to make a competitive appearance for United this season after being injured in training prior to the Premier League opener against Birmingham on Aug 16.
Old Trafford manager Sir Alex Ferguson has already ruled Ferdinand, 30, out of this weekend's home clash with Arsenal and the defender is almost certain to miss England's forthcoming fixtures against Slovenia and Croatia next month.
But having started jogging at United's Carrington training ground on Monday, Ferdinand is now hoping to return in time for the Premier League clash with unbeaten Spurs at White Hart Lane on Sept 12 - a week before his initial planned comeback against Manchester City at Old Trafford.
Ferdinand said: "It (the injury) is improving and I'm a bit ahead of schedule.
"I've been training really hard the last few days. I'm not where I want to be obviously on the pitch, but in a couple of weeks, I'll be back on the pitch playing again.
"Hopefully the match after the internationals I will be fit so that's what I'll be aiming for. At the moment I'm concentrating on that."
United manager Ferguson is facing defensive worries for the game against Arsenal.
Northern Ireland international Jonny Evans is a doubt with the ankle problem that will ultimately require surgery, while Gary Neville and Wes Brown are still short of full match fitness following pre-season injury lay-offs.
Saturday's game against Arsene Wenger's team, who face Celtic in the Champions League tonight, will be the first 'Big Four' clash of the season and, although Ferguson admits that such fixtures are crucial in the title race, he insists that the Christmas period is key.
Ferguson said: "I always look for the games near Christmas and the run-in - the last four or five matches.
"They're the ones that I look for first because that Christmas period can be tricky.
"But then I have a look for the games against our big rivals - Chelsea, Liverpool, Arsenal and Manchester City.
"The thing that can make life difficult is if you have to play in Europe on Wednesday and then away on a Saturday lunchtime. That's tough."