Golf World cited unnamed sources as saying Bank of America, in its first year as the title sponsor, wants Sorenstam to play. The Colonial is May 22-25 in Fort Worth, Texas.
The 32-year-old Swede, who last year won 13 times around the world and shattered the LPGA Tour scoring average, said two weeks ago that she would love to compete against the men if offered an exemption.
``I have nothing to lose,'' Sorenstam said. ``It would be a challenge.''
Her only stipulation was to play on a course where she would not be at a huge disadvantage off the tee. Colonial is only 7,080 yards, although it plays to a par 70.
Messages left for Sorenstam's agent and her husband by The Associated Press were not immediately returned.
Tournament director Dee Finley suggested last week that Colonial had no room for Sorenstam because it had several players interested in their exemptions and ``we're here to provide a place to play for PGA Tour players.''
``It would be fun to see her play, but I'm afraid that will not be possible for Colonial this year,'' Finley said at the time.
On Monday, Finley told Golf World that talks had reached an advanced stage.
The last woman to play a PGA Tour event was Babe Zaharias in the 1945 Los Angeles Open. Zaharias not only qualified for the tournament, she made the 36-hole cut until a 79 eliminated her for the final round.
If Sorenstam were to play Colonial, she would steal the spotlight from Connecticut club pro Suzy Whaley, who has said she will play in the Greater Hartford Open in July.
Whaley qualified by winning a PGA of America sectional tournament, even though she was allowed to compete from a shorter set of tees. She has indicated she would not at all mind if Sorenstam made her men's-tourney debut before her own.