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.
Mr Rodgers said: "They are not too far away, but then that is a matter which is out our hands. Having received them in such a short period of time, however, is an indication of the level of qualified interest in this particular property."
McIlroy, 23, the world's No 1 golfer, put the house up for sale in September after deciding he would be spending virtually all of his time overseas. He has not been back since the For Sale sign went up.
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.
His five-bedroom property at Moneyreagh in the Castlereagh hills above Belfast was built in 2006 at the height of the property boom, and sits on a 14-acre estate. It includes a gymnasium and a golf practice area as well as a driving range and putting greens with different types of grass.
McIlroy is said to have thought long and hard about the sale, but made the decision on "purely practical and commercial reasons". He once shared the house with his former girlfriend Holly Sweeney - they separated last year - but is now in a developing relationship with tennis star Caroline Wozniacki.
In a brochure produced for the sale, McIlroy is quoted saying: "I have really enjoyed living here. It is a really special place which has allowed me to relax and unwind - when I get time!"
McIlroy is spending Christmas and New Year with his girlfriend, but any time he returns to Northern Ireland he plans to stay with his mother and father, Rosie and Gerry McIlroy, in Holywood.