Premier League leaders United have already secured first place in the group and the home clash against the Romanians could offer a chance to rest key players ahead of the weekend's derby at Manchester City.
Romanian club Cluj are still vying with Galatasaray for a place in the last 16 so there will be a competitive edge to the game.
Ferguson had hoped the influential Vidic, out since September after undergoing knee surgery, would be available to help shore up a defence that had been leaking goals.
However despite taking part in training on Tuesday, Vidic needed more time, Ferguson said.
"I don't think Nemanja will play," the Scotsman told the club's website.
"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.
"I wasn't considering Nemanja for Sunday [against Manchester City] anyway. Playing tomorrow would have been a bonus but Sunday would have been too soon [for that sort of game]."
United have conceded 21 goals in 15 Premier League matches this season - only Tottenham Hotspur in the top half have conceded more - and the return of Vidic would have been a huge boost with the hectic Christmas schedule looming.
Ferguson said England striker Rooney would be involved as he needed games to get to his best form.
"When Wayne gets interrupted he needs three games to get back," he said. "That's why he'll definitely play tomorrow.
"Wayne needs to play a lot of games to get his match-fitness up. He's a strongly-built lad and when he misses two games, it takes him three games to come back. It's the way he's always been."
United, who are three points clear of City in the title race, are past masters at reaping a large haul of points around the turn of the year and Ferguson, while having one eye on Cluj, is looking forward to more of the same.
After City, United welcome Sunderland to Old Trafford and then the Reds travel to Swansea City before completing 2012 with home games against Newcastle United and West Bromwich Albion.
"It's generally a good month for us," Ferguson said earlier.
"We usually get ourselves to the New Year in a challenging position and that's where you want to be. When you have the second half of the season in front of you, you know full well that pressure can affect everyone, there's no question about that. We tend to do not too badly.
"The start of the month, with City away, is a hard one, but then we've got Sunderland, Swansea, West Brom - we've got a reasonable programme, so we should be expected to gather some points there."
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