Golfweek magazine reported Monday that key players stated in the letter the LPGA Tour's woes cannot be blamed on a poor economy, and they said the tour should find a new leader to rebuild relationships with longtime sponsors.
The magazine cited a player who had received a copy of the letter.
Among those at the meeting last week in Toledo, Ohio., were Lorena Ochoa, Paula Creamer, Cristie Kerr, Morgan Pressel and Natalie Gulbis, among the most prominent players in women's golf.
Golfweek said players in favor of Bivens' resignation attached their names, although it didn't say how many signed it.
LPGA spokesman David Higdon did not immediately respond to an e-mail seeking comment.
The meeting came two days after the LPGA Tour lost another tournament when the Kapalua LPGA Classic asked for a year off to find a title sponsor. Instead, the LPGA said it would use all legal remedies to hold Kapalua to the remaining four years of its contract.
The tour has left two stops ' Rochester, N.Y., and Toledo ' uncertain if the contracts will be renewed for next year, and it already has lost the popular Corning Classic. Also up in the air is the Michelob Ultra Championship in Virginia.
The LPGA has lost seven tournaments since 2007, including all three events staged in Hawaii.
Seoul Broadcasting Systems was offended when Bivens announced during the SBS Open in Hawaii that it had a new television contract with another Korean network. That ended SBS' sponsorship, and it then signed a 10-year with the PGA Tour to sponsor the season-opening tournament at Kapalua, won this year by Geoff Ogilvy.
The U.S. Women's Open, which is not run by the LPGA Tour, is being played this week outside Philadelphia. After that, the LPGA Tour will not have another tournament in the United States until the last week in August.
Golfweek reported that at a player meeting last month at the State Farm Classic, players were told 10 contracts with title sponsors had been signed for 2010.
'We're getting to the point where we don't know who to believe, which is hard,' Katherine Hull told the magazine. 'When tournaments that have been very loyal to us start withdrawing, that's really a red flag to me.'
Bivens, who took over for Ty Votaw in 2005, has two years remaining on her contract.