At a meeting of Dungannon District Council permission was sought to apply for a loan to make up a funding shortfall for the heritage site.
The council has already secured a grant of £2.3 million from the Heritage Lottery Fund, but needs to raise a further £3.2 million if its plans for a park and arts centre are to go ahead.
It is hoped that a grant from the Arts Council will reduce the amount the council needs to raise from ratepayers.
The total costing for the scheme, which is intended to help regenerate the town centre, is £5.5 million.
Acting Chief Executive of the Council, Ian Frazier, said that development of the Castle Hill site would benefit everyone in the borough.
"We are in the final years of this council's existence and we are keen to leave behind the legacy of a civic building for community use", he said.
"The park will also help regenerate the town centre. The feedback we have got from community groups is that the scheme would be welcomed."
Mr Frazier acknowledged that the costs might seem burdensome given the current recession.
"The council will have to secure a loan for around £2.5 million, and service it like a mortgage through revenue costs over a period of fifteen years."
He went on to say: "However, if the council decides the cost is too prohibitive we will not go ahead with the plans."