Sports Business Daily, citing sources, reported on its Web site that the LPGA Tour board has authorized a golf industry executive to contact potential candidates to replace Bivens.
The sports trade daily reports the tours board was not actively negotiating a buyout, but talks are expected to begin soon.
The LPGA infighting has overshadowed what should be the biggest week of the season in womens golf, the U.S. Womens Open, which kicked off Thursday.
Bivens is owed $500,000 per year for the final two years of a three-year extension she signed in 2008, the report said.
An LPGA spokesman did not immediately return a phone message or respond to an e-mail seeking comment.
More than a dozen players, including top-ranked Lorena Ochoa, sent a letter to the board seeking Bivens resignation. In the letter, the group said the tours problems cant be blamed on the dismal economy and a new leader is needed, according to Golfweek magazine, which broke the story Monday.
The tour has lost seven tournaments since 2007.
The talk in the days leading up to the start of the championship at Saucon Valley Country Club was as much about the controversy as it was course conditions.
Players at the Womens Open have been peppered with questions about the letter, Bivens and the tours future. Most have sidestepped the issue, citing respect of the USGA event.
Ochoa didnt hide her concern for the future of the tour and called for more player participation in moving the organization forward.
We as players, we want to be more involved in what is happening and we want to see the tour going in a better direction, Ochoa said Wednesday, on the eve of the first round.
Theres not much we can do. I believe they will do the best for us, and hopefully things will start, you know, moving in a good direction, because we are worried that were losing tournaments and we want to get back on a good track.
Suzann Pettersen acknowledged signing the letter calling for Bivens to step down.
All we are doing is standing up for our tour, Pettersen told Golfweek Magazine. Now its up to our leadership and our board to find a solution.