Manchester United's Champions League second-leg against Real Madrid on 5 March.
Jones suffered an ankle injury during Monday's FA Cup win over Reading and is having intense treatment in the hope of being available for the Old Trafford match.
Ferguson said: "We are working very hard. He has an outside chance for Real Madrid - no more than that. He is a young man who went into a tackle too brave and was a bit off-balanced. He certainly won't be fit for the weekend."
Ferguson, who reported that everyone else had come through Monday's match without a problem, also spoke publicly for the first time about David Gill's decision to stand down as chief executive.
"David spoke to me about it some weeks ago. I was surprised because he is still a young man but I understand where he is coming from. Sixteen years in that particular job is not easy."