One has been lodged by an international businessman with interests in Northern Ireland and a second from someone in London who is planning to return home.
Estate agent Michael Rodgers, from Holywood, Co Down, who is handling the sale, said he expects a deal to be completed early next year.
He said: "All the people who have viewed this property are capable of buying the house. We've had no time-wasters."
Another viewing is planned for next month. The current offers are believed to be within range of the asking price of £2m (€2.4m). Mr Rodgers said: "They are not too far away, but then that is a matter which is out of our hands."
McIlroy (23) the world's number one golfer, put the house up for sale in September after deciding he would be spending virtually all of his time overseas.
According to reports in the US, he is buying a $10m (€7.6m) mansion at Palm Beach Gardens, Florida, located near the exclusive The Bear's Club where he works on his game.
The property measures 10,000 square feet, has six bedrooms, nine bathrooms, a dock and putting green, and was built three years ago.
McIlroy is said to have thought long and hard about the sale, but made the decision on "purely practical and commercial reasons".