Cornelius, who arrived at the club in the close-season for a reported then-record fee, has only featured in two competitive games for Cardiff, having injured his ankle in the League Cup win over Accrington Stanley in August.
Mackay confirmed the Denmark international striker has returned to the squad, explaining that this weekend's game against the Premier League champions is one that everyone at the club is anticipating.
"Andreas is back in the squad and back in training. He had a good 60 minutes against Yeovil (in a behind-closed-doors friendly) last week," he said on Friday.
"(Saturday's game is) another one the whole city, the fans and myself are all really looking forward to.
"(Manchester United) are certainly in a good vein of form. It's one we're all relishing and looking forward to."
Defender Ben Turner echoed Mackay's excitement ahead of the clash, although he insisted he will not be overawed by United's front pairing of Robin van Persie and Wayne Rooney.
"I don't see them as the toughest test, just a different test. In the Premier League there are so many great frontmen," he said.
"Every week is a different personal challenge. Every team has some of the best players to test yourself against.
"They've been on an excellent run recently and will obviously provide a massive test on Sunday."
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