A final report is expected from Uefa following a visit by officials to Belfast over proposals to host Euro 2028 tournament games in the city.
Stormont Economy Minister Conor Murphy also pressed for the release of tendering documents around the redevelopment of Casement Park for the tournament to reveal projected costs.
There has been uncertainty around funding for the project with some reports suggesting it could cost as much as £308 million (€360 million).
In 2011, the Stormont Executive committed £62.5 million to the project.
In February, the Irish Government offered £40 million towards it, and the GAA has said it will contribute up to £15 million.
Last week, Northern Secretary Chris Heaton-Harris said the British government is “working to figure out” how much the renovation of Casement Park will cost, with recent prices “significantly higher” than they were a year ago.
He added: “Any taxpayer contribution to the Casement Park project will need to be made on a value-for-money basis, and I’ve said also many times there is no blank cheque here, especially when there is no contractor appointed yet, we do not want to artificially inflate a price.
“The Northern Ireland Executive will also need to decide on whether and how it will underwrite any future increases in cost, so we are all, all partners are working together to try and figure out what the number is and how we can deliver on it.”
Speaking during questions for his department in the Stormont Assembly on Monday, Mr Murphy said officials from his department, along with those from the Department for Communities, the IFA and the GAA, met with a Uefa delegation in Belfast in February.
He said since then there has been “further engagement 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.
“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.”
SDLP MLA Justin McNulty pressed Mr Murphy on the uncertainty around funding.
Mr Murphy responded saying he would like to see tendering documents released, contending that would give “more certainty in terms of what the actual cost of the project will be”.
“I met recently with both the IFA and the GAA myself, and there is a concern that any delays in relation to this will potentially dent confidence from Uefa for whose decision it will be whether hosting the games here or not,” he said.
“So I’d like to see that moving at pace and moving as soon as it can possibly happen.
“I understand the Communities Minister [Gordon Lyons] is engaged with the British government in terms of their contribution, but I don’t think that that should necessarily delay the release of tender documents.
“I think if those documents were released, then we would get a clearer sense of what the actual costs might be.”
