Blues have had the pleasure of the Tring official in two of their Premiership games so far this season.
The last of those games was in the home defeat to Blackburn Rovers back in December when Blues striker Christophe Dugarry was sent off for two yellow card offences.
Mr Barber also refereed Blues away draw at Wolves in November and Dugarry was also cautioned during that game at The Molineux.
Sunderland fans last saw Mr Barber at The Stadium of Light in their 3rd round victory against Hartlepool when Julio Arca was shown a yellow card in the 1-0 win over their North-East rivals.
In total Mr Barber has refereed 19 games so far this season, showing 55 yellow cards and 2 reds.