A 1-0 defeat to Manchester United on Saturday leaves the Canaries four points adrift of safety with two games left to play.
It means that anything less than victory over Watford on Wednesday will see Neil's side drop back into the second tier, although even a win at Carrow Road will not be enough to save them should Sunderland triumph over Everton at the Stadium of Light.
But Balls, who took the role of chairman at the club just after Christmas, insists they will stick by their current boss no matter what the outcome at the end of the season, although he did hint that changes were likely.
He told BBC Radio Norfolk: "Alex Neil is one of the best managers in British football. He's got our 100 per cent support for this week and also in the coming months as we deal for next season.
"But clearly it's been messy. When there's speculation all over the place, the board has to stand back and ask what's happened and what's our responsibility?"
While Neil could be in line to stay in East Anglia, the same cannot be said for chief executive David McNally, who announced his resignation following their latest defeat, much to the surprise of the City hierarchy.
"Nobody expected after [Sunday's] Manchester United game we would lose our chief executive," Balls added.
"It's been very destabilising to the club. But we've got to make sure going forward the football club keeps going from strength to strength.
"The directors had a discussion over the course of Sunday and decided with great regret to accept that resignation."