It is understood the outgoing Policing Board has written to the prime minister asking him to address a cash shortfall for the new police training college.
Training will start at the centre in 2009
The college, due to be built near Cookstown, is expected to be operational by late 2009.
The project was estimated to cost around £130m, but the government has only secured funding of £90m.
Policing Board members said the shortfall was delaying the putting of the project out to competitive tender.
Some board members claim that architects and others working on outline plans "have been put on hold".
It is believed the leaders of the DUP, the Ulster Unionists and the SDLP have all written to Downing Street asking the government to address the problem.
The DUP's Ian Paisley Junior said the project was "at crisis point".
Mr Paisley, a member of the Policing Board, said it was the government's responsibility to meet the £40m shortfall in funding for the new college.
He said police should not "have to put a begging bowl out" in the Irish Republic or the United States to fund the college.
SDLP policing spokesperson Alex Attwood MLA said the prime minister and the chancellor should "get their heads together and find additional monies" for the college.
"The £90m currently identified by the NIO is from existing budgets," he said.
"Not one extra penny has yet been released by the London Exchequer."
A police spokesperson said the PSNI was "determined and committed" to ensuring the new college was "a centre of excellence and a new beginning for police training" in Northern Ireland.
"A substantial part of the funding has been identified and earmarked for the college and we are seeking additional funding needed," the spokesperson said.
"To date, the land acquisition has gone ahead, the legal work has gone ahead and planning is continuing on the basis of the funding identified."
The academy, due to be built on a 270-acre site near Cookstown, County Tyrone, was scheduled to be operational by 2008 but will not now be finished until 2009.