The Serbian has been sidelined since September after undergoing knee surgery but looked to be winning his fitness battle ahead of the clash with Manchester City on Sunday.
However, the Scot feels that Vidic still needs more training under his belt before he can return to first-team action and believes that, if he does not feature against Cluj, he certainly will not be ready to face the Premier League champions.
He told reporters on Tuesday: "I don't think Nemanja will play. He feels he needs another few days' training so he won't be available.
"He's not far away. He's training well now but I think another few days will bring him on better. If he doesn't play tomorrow there's no chance he'll play in the derby game."
After a frantic 4-3 win over Reading on Saturday, Sir Alex added: "I think we're getting punished when the ball's going into our box at the moment but we should be defending far better, albeit Reading produced some fantastic balls into the box. We should be expecting better. It's a worry.
"If we perform like that on Sunday then God knows what's going to happen to us. When you see the goals against - we've lost 32 already - I can't remember us losing so many goals before Christmas.
"It's a concern, there's no question about that. When you see City have [Mario] Balotelli, [Edin] Dzeko - all really tall players - it's going to be a big challenge. But that's on Sunday. Tomorrow we've got a different game."
The United manager also revealed that Shinji Kagawa is close to a return and could be included on the bench against City on Sunday but that he will not play any part against Cluj.
"Kagawa started running today. He may make the bench [against City]," the veteran boss continued. "Obviously Nani and [Antonio] Valencia are still out and that's why I played [Wayne] Rooney on wide right [against Reading] - I thought it was his best performance of the season.
"Against Cluj I'm picking a team without any thought of Manchester City. It's a matter of who needs a game."
|"Kagawa started running today. He may make the bench against Manchester City"
- Sir Alex Ferguson on Shinji Kagawa
With United's place in the last 16 of the Champions League secure, Sir Alex confirmed that he will make several changes to his normal line-up but intends to put out a side capable of winning the match.
"The situation Cluj are in is that they lost to Galatasaray at home, which puts Galatasaray in a stronger position, but Cluj still have an opportunity if they beat us tomorrow," he warned.
"It's very tight - there's not much between all three other teams. That's been shown in the tightness of the group.
"We'll rest some players tomorrow, as we did against Galatasaray, but we have to be fair to all the teams who are trying to reach important positions - whether that's the Champions League or the Europa League."