Jones was taken off the field with an ankle injury during the FA Cup fifth round tie with Reading, at the time the reports said that he would be odds on to miss the game.
But the England international is making progress in his battle to be fit, although the boss does recognise that he will have to put in some hard work between now and the game to stand a chance of being included in the squad.
“Phil Jones starts running today,” Ferguson told reporters ahead of Saturday's game with Norwich.
“He’s got a fight on his hands to be ready for Tuesday but we’ll give him every chance. He won’t be available for tomorrow.”