McIlroy’s current endorsement deal with Titleist expires in December, and the 23-year-old could sign a 10-year contract worth £156 million, or $250 million, according to the Daily Mail.
Woods, who will play McIlory in an exhibition match in China on Monday, currently has a lucrative deal with Nike that pays him roughly $20 million a year. He signed with Nike in August 1996 when he first became a professional golfer, but when his personal life hit the front pages, Woods and his public image slowly dwindled.
In 2009, Woods' extra-marital affairs came to light and he subsequently left the PGA tour to deal with his divorce and personal problems. Many of his sponsors like Gatorade and General Motors dropped Woods, but Nike continued to support the 14-time major champion.
When asked about the rumored deal, the No. 1 ranked player in the world was mum on the subject.
"These rumours have been going around for years and it seems to always come up at this time of the year," McIlroy said to AFP. "I leave it up to Conor (Ridge, McIlroy's manager) to sort out as it leaves me to concentrate on my golf.
"That's all I can do and besides I have enough to think about trying to get the ball in the hole. Also I've got a very important end to my season coming up and I need to concentrate myself fully on that goal."
McIlroy had perhaps his most successful year as a professional in 2012, capturing the PGA Championship in August, and earned the top spot on the money list with almost $2 million more than Woods.