''We'll have the cash on the tee if she wants to play,'' Riegger said after the first round of the Capital Open.
Two weeks ago, Sorenstam became the first woman in 58 years to play a PGA Tour event. She shot rounds of 71 and 74 and missed the cut at the Colonial, finishing tied for 96th and ahead of 11 other players.
''She made a statement in her press conference that she had last week, that if she played 30 events on the tour she could finish the top 100 on the money list,'' Riegger said.
''I've been playing professional golf for 18 years and this is my seventh year on the tour. I've never finished in the top 125. I've always been in the 126 to 150 category, so I just made a challenge to her.''
Riegger said the challenge would be stroke play over 18 holes with both players using the same tees. He said Sorenstam could choose the time and place.
''Anywhere, anytime,'' he said.
Riegger said he was unsure whether his intermediaries have contacted Sorenstam. Sorenstam played Thursday in the LPGA Championship in Wilmington, Del., but she finished her round by the time Riegger spoke and was unavailable for comment.
Riegger said he has people in Las Vegas ready to put up the money, but he wouldn't say who they are.
''Who knows where it's going to go?'' Riegger said. ''It could turn into a pay-per-view event, and neither one of us have to put up any money.''
Riegger, who turns 40 next week, is playing in just his fourth PGA Tour event this year, having made the field at the Capital Open as the seventh alternate. He finished in the top 20 in both Houston and New Orleans and failed to make the cut at Pebble Beach.
His best career finish is an eighth-place tie at last year's Honda Classic. His best end-of-year finish on the money list is 140th in 2001.
''I think the general public has a misconception of how hard it is to finish in the top 125, let alone the top 100 in the money list,'' said Riegger, who shot a 1-over-par 71 Thursday.
''I thought she played great at Colonial. I was pulling for her. I don't have anything against Annika. It's just a statement she had. I just don't feel like that's right. ... I think it's a little far-fetched.''
Riegger said he had no idea whether Sorenstam will accept.
''I've got more to lose than her. I'm supposed to beat her, I guess,'' Riegger said.
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