The second Northern Irish golfer to lift the title, Councillor Muir has previously pushed for his sporting achievements to be acknowledged in Holywood Town Centre.
He said: “I offer the warmest congratulations to Rory McIIroy on his Irish Open Win, which is not only a fantastic personal success, but also a reason for great pride for the people of Holywood and beyond.
“Rory is an outstanding ambassador for Northern Ireland and his donation of £515,000 to charity is a testament to his sense for generosity and commitment to those in need. That’s why I’ve previously requested that the Council explores how to best recognise his achievements in the long term.
“With a report being prepared, I’ll be following this up immediately to see if we can progress this further and give Rory McIIroy the recognition he deserves as one of the world’s top golfers.”