The announcement follows an unsuccessful application to the Heritage Lottery Fund.
Councillors have since met with representatives from the funders for feedback, and to explore other opportunities.
Lottery officials said the application was both comprehensive and professional, however there was a limited amount of funding available for the whole UK.
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It was recommended that the council considers dividing the original application for the Palace Park into smaller projects.
Armagh Mayor Thomas O'Hanlon said: "The Palace Grounds belong to everyone across the city and district and we want to open up the grounds to the people and make it public space that everyone can enjoy and take ownership of.
"Councillors want to see the grounds being used on a daily basis by local residents, be it for walks, sports or major events."
He continued: "We've had a minor setback with the first funding application being unsuccessful. But we're determined to make this project work; we haven't given up on the Palace Park.
"The council has agreed to pro-actively source alternative funding for the project, only in smaller individual projects and we have considered some priority issues such as lighting, seating and signage."
(PR/BMcC)
