Both ISPs are concerned that the state-funded network will impact investment in their commercial rollouts.
The government broadband investment pot to provide ten cities - including Birmingham - 'ultrafast' broadband (up to 100Mbps) and high speed wireless access.
Birmingham required state aid approval from the European Commission (EC), which it was granted, and revealed that it would focus on businesses in Digbeth, Eastside and the Jewellery Quarter.
Sir Albert Bore, leader of Birmingham City Council, said at the time of the EC's decision that the green light would benefit residents and businesses in the future.
He said: "This will put Birmingham at the forefront of the race to deliver public services in new and innovative 'Smart' ways.