The Red Devils manager has confirmed that the Serbian defender is able to prepare with the first team once again, and also welcomed the introduction of goal-line technology
The United boss also revealed that Jonny Evans was back in full training this week following injury at Sunderland in late March, while Chris Smalling could only manage light fitness work.
Paul Scholes, who has taken longer to recovery from a routine knee procedure than was expected, is scheduled to train on Monday.
"I'm hoping Vida will start training [Friday]," Sir Alex told reporters. "Jonny Evans has trained this week, which is better news than we had building up to Monday's game.
"Ashley Young is out – he got a sore whack on his ankle and is maybe out for two weeks. Other than that, we're in good shape in terms of player availability.
"Chris Smalling started running this week and Paul Scholes will start training with the first-team on Monday. He's done a fair bit in the last week or so and it will be a terrific boost to get his football intelligence back in the squad. He's been out for a few weeks now so he'll need a good bit of training with us."United travel to Stoke on Sunday on the back of Manchester derby defeat at the hands of City, and the importance of the match is not lost on the 71-year-old.
"We have a job to do," he added. "The incentives are there for ourselves in the sense of we've only got seven games left.
"The challenge is there for Stoke as well. I don't think they will go down but, nonetheless, they're in a precarious situation because, down the bottom of that league, you don't pick up a lot of points. I think they'll get enough to get out.
"I don't think we should look at our position in terms of being 12 points clear.
"As we always do, we should just try to do our best. We have a job to do on Sunday and we need to do it.""It's always a difficult place to go, but we have a job to do. Stoke have a great support, probably one of the noisiest in the league.
"You know you’re always going to get a hard game at Stoke. That will never change."
And Sir Alex, who claimed that there "there was nothing between the two teams" during Monday's loss, has backed the imminent implementation of goal-line technology in the Premier League.
"It had to happen. It's time football caught up."