Vieira, who captained Arsenal to three league titles and four FA Cups as a player, was sacked by French Ligue 1 side Nice in December.
Chelsea lost 2-1 at Aston Villa -- a result that could have been curtains for them in the top-four battle. Yet they were saved as arch-rivals Tottenham twice came from a goal down to win 4-2 at Leicester City.
United's defeat means City are 10 points clear with both sides having three games left to play.
United's win put on hold the title celebrations of champions-elect Manchester City.
With Chelsea looking secure in the top four, the final Champions League place looks to be a three-way fight between Leicester, West Ham United and Liverpool.
Fans stormed the stadium and pitch before kick-off in protest against the club's owners - the Glazer family.
The news comes the morning after the London club said it was one of 12 clubs forming a breakaway European Super League.
The result ended City's six-game winning streak in all competitions as they remained on 74 points, 14 clear of second-placed Manchester United at the top of the standings having played two more games.
The report said the pair squared up to each other after Rudiger went in late on the goalkeeper and that they had to be separated by teammates. The defender was then sent to the changing room five minutes before the end of the session.
City now need, at most, 11 points from their remaining seven matches to secure their third Premier League title in four seasons.