UEFA is expected to release a final report on Casement Park hosting Euro 2028 matches within weeks.
The report follows a visit to the west Belfast site in February by officials from the soccer governing body.
Economy Minister Conor Murphy met with the UEFA delegation during the visit, alongside representatives of the GAA and the Irish Football Association.
Questions remain over the cost of the long-awaited project, which some reports suggest could be as much as £308 million.
Stormont committed £62.5 million to the project in 2011, while in February, the Irish government offered £40 million under Shared Island funding. The GAA has said it will pay up to £15 million towards the new stadium.
The British Government is expected to contribute, but last week Northern Ireland Secretary Chris Heaton-Harris said that London is “working to figure out” on how much the renovation of the site will cost, as estimates were “significantly higher” than they were a year ago.
He said any taxpayer contribution to the project “will need to be made on a value-for-money basis” and said there was no “blank cheque” available.
Speaking at Stormont on Monday, Mr Murphy said there has been “further engagement” with UEFA and “significant progress has been made, including detailed plans that demonstrate how a redeveloped Casement Park can host games during Euro 2028″.
“We now await a final report from UEFA expected by early June in response to these proposals,” he said.
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“This tournament is estimated to generate £2.6 billion in benefits across these islands with games due to be hosted in Belfast and Dublin, it creates a fantastic opportunity to promote the island of Ireland to a worldwide audience of over six billion people.
“The work is progressing well. The Ulster Council of the GAA has commenced site clearance work, and that’s a very welcome and proactive move on their behalf.
“They have committed £4 million of their own money to keep this project alive, and it’s a clear demonstration of their commitment to being a positive and active contributor in bringing the Euro 2028 international soccer tournament to Belfast.”