Ferguson stepped down as the Red Devils' manager back in May and was subsequently replaced by David Moyes, and Schmeichel feels that the upheaval at Old Trafford has lifted their Premier League title challengers.
"Every club would think they have a chance now," Schmeichel told reporters. "Manchester United have lost the most important person the club has had for many decades [and] other clubs have been out there spending a lot of money.
"It is interesting because obviously of the big changes at United. Edward Woodward has taken over as the new chief executive and David Moyes has taken over as manager.
"We don't really know how it is going to go. But Manchester United is Manchester United and we always manage to pull through."
United begin their title defence with a trip to Swansea City on August 17.