The centre back has not played for the Premier League leaders since injuring his calf in the warm-up before the 2-1 defeat by Wolverhampton Wanderers on February 5.
United's pursuit of a record 19th English league title, as part of a potential treble with the FA Cup and Champions League, has been hit by a string of injuries to defenders in particular.
Rafael has also started training but will not be available for Saturday's trip to struggling West Ham while fellow defenders Wes Brown and John O'Shea are expected to return to training on Monday and Jonny Evans is suspended.
"It still leaves us considerably short for tomorrow in terms of the right-back position, we'll have to solve that," Ferguson told a news conference.
"I thought the two-week break (for internationals) would bring a few of them on, and it has, but not enough to play tomorrow."
Ferdinand was delighted to be close to a return, writing on Twitter: "(I am) buzzing to be out on the training pitch again".
The 32-year-old could feature in next week's trip to Chelsea for the Champions League quarter-final first leg but looks more likely to return for the league match at home to Fulham on April 9.
"He has only been training two days and then just a light session today," added Ferguson. "He is more likely to be fit for Fulham."
THREE COMPETITIONS
Brazilian Anderson will travel with the team to West Ham but fellow midfielder Darren Fletcher is grappling with a bad virus and will be assessed next week.
The back four is boosted by the return from injury of captain Nemanja Vidic who is likely to be partnered by Chris Smalling as United seek to tighten things up having lost 4-0 at Upton Park in the League Cup this season.
Ferguson's men are seeking to repeat their 1999 treble but the injury situation is a worry.
"It's great to be involved in three competitions," said the manager. "The difference in '99 was that no one was injured. That was the benefit we had then, the advantage.
"These next couple of weeks are crucial for us to get all these players back. If we get them back then it definitely enhances our chances, there is no question about that."
United have 63 points, five ahead of second-placed Arsenal who have a game in hand. They could go eight points clear, for a few hours at least, if they beat West Ham as the Gunners host Blackburn Rovers later in the day.
