There had been problems over costs, incurred by the design team working on the project.
Planning permission for the site, just outside Cookstown, was granted in January.
It will be NI's first police, prison and fire officer training centre.
The 23,000 square metres facility will provide new teaching, training and residential facilities.
In response to a question by the SDLP's Patsy McGlone, Mr Ford said there had been a "relatively short slippage" in the time to complete the work.
"The delay is currently being looked at a period of four months with an expectation that construction can begin by the month of October, so given the very significant cost change, I believe that's a fairly reasonable position to be in, and I'm optimistic that that can be adhered to," he said.
It was revealed in March that "professional incompetence" by the design team working on the project has lead to the costs spiralling by more than a third - from £101m to £137m.
The justice committee was told mistakes over how the project was costed was the reason for the soaring bill.
To counter-act the rise in costs, Mr Ford said changes were being "worked through" to some of the planned specifications to save as much money as possible.
"Something like the motorway training area was originally to be constructed to full motorway standards," he said.
"The reality is that its use in training will result in considerably less wear and tear than would happen on a motorway carrying several thousand vehicles a day, so that's an issue where it's been possible to keep the core facility whilst reducing the cost of construction quite significantly."
The project was first announced in 2004 and was originally due to be finished in 2008. The cost envisaged at the time was £80m.
Justice Minister David Ford has said he is optimistic work on the long-awaited £130m training college at Desertcreat, County Tyrone, will finally begin in October.