Transport Secretary Grant Shapps announced he is evaluating a proposal from the train operator on options for continuing its franchise.
"Following completion of this process I will consider whether to award ARN (Arriva Rail North) a short-term management contract or whether to ask the Department of Transport's own operator of last resort to step in and deliver passenger services," he said.
Chris Burchell, Arriva's managing director of UK Trains, said: "We accept services on the Northern network are not yet good enough and we sincerely apologise to our customers for our role in that.
"Many of the issues affecting the franchise however are outside the direct control of Northern. Assumptions were given when the plan for the franchise was developed that critical infrastructure projects would be delivered to enable growth and support capacity demands.
"Many of these have either been delayed or cancelled. This, along with unprecedented levels of strike action, has had a significant impact on the franchise - both in terms of service and financial performance.
"These challenges will continue to affect services irrespective of who is running them.
"What is needed is a new plan and, in that analysis, we are fully in agreement with Government. That is why the Government asked us to prepare a business plan for a shorter 'Direct Award'."
Mick Cash, general secretary of the Rail, Maritime and Transport union, said: "This is just another fudge by the Tory Government on Northern but it still proves without a shadow of a doubt that their private franchise model for running our railways is finished.
"The whole privatisation experiment which has reduced our railways to chaos must now be consigned to the dustbin of history.
"Other basket cases - South Western Railway, Scotrail, Trans Pennine Express and the rest - should also be put out of their misery and be brought into public ownership as soon as is practically possible and I have written again to the Transport Secretary to discuss exactly that.
"This nonsense cannot go on. Today's decision by Grant Shapps makes a mockery of the imminent Williams Review which didn't even consider the public ownership model.
"The spivs and speculators who have spent 25 years bleeding Britain's railways dry should be told that the game is up for every single one of them and should be instructed to pack their bags and clear out."
Manuel Cortes, general secretary of the Transport Salaried Staffs Association, said: "This non-statement from the Government is a complete betrayal of long-suffering Northern Rail passengers.
"Instead of a 'short-term option' to be announced later in the month, the Government should do the right thing now and immediately bring Northern Rail into public ownership. It's blindingly obvious to anyone with an understanding of the extent of the failure of Northern Rail that the positive proven record of public ownership is what is required and what passengers and staff deserve.
"Even now, with a decisive majority, the Tories are wary of undoing their Frankenstein privatisation of our railways as it runs against their ideological DNA, even though everyone knows the current system is broke beyond repair. The Tories are already failing the North."