Manuel Cortes's comments come after a report from the Campaign for Better Transport called for Arriva Northern to be nationalised..
Keith Williams, who’s heading a review of Britain’s railways, will shortly report to the government.
Mr Cortes said: “The franchise model has failed and Northern just happens to be the worst of a bad bunch. The Government can’t go on looking the other way armed only with sticking plasters.
“I recently met Keith Williams and told him this face to face. He has a golden opportunity to improve the lives of millions across the North by telling Transport Secretary Grant Shapps that the game is up and Northern must return to public control. Frankly that is the only way to turn this mess around and create a system which works for passengers rather than profiteers."
A Northern spokesperson said: “Our customers deserve the best possible rail service and we are working hard, to improve industry performance.
“Arriva and Northern remain fully committed to delivering the transformation of the North’s railways and improving customers’ experience. We are delivering the biggest transformation of local rail for a generation, with 52 of our 101 new trains now in service."
A Department for Transport spokesperson said: “We are developing contingency plans for the replacement of the current franchise with either a new short-term management contract with Northern or the 'Operator of Last Resort'.”