Ancestry.com Inc., the family- history research website, has asked potential buyers including Permira Advisers LLP and TPG Capital LP to increase their competing bids for a possible buyout.
Talks are ongoing and a deal might not materialize.
Ancestry.com turned down a bid of $35 a share.
KKR & Co. and Providence Equity Partners Inc. expressed interest early on yet didn't submit bids because they consider the price too high.
Ancestry.com's shares have surged 34 percent since June 5, when Bloomberg reported that the company had hired Frank Quattrone's Qatalyst Partners LLC to find buyers.
Heather Erickson, a spokeswoman for Ancestry.com, declined to comment. Representatives of Permira, TPG, KKR and Providence declined to comment.
Ancestry.com reported second-quarter sales and profit last month that topped analysts' estimates, citing user gains and demand for new products. The company raised its sales forecast for 2012 to as much as $480 million and said it passed the 2 million-user milestone in the period by providing access to more information, including on DNA and U.S. census figures.
Ancestry.com was founded in 1983 as a publisher of genealogical books and magazines, and later digitized its content.