Blackstone Group LP, Thomas H. Lee Partners LP and TPG Capital are in talks to pay more than $15 billion including debt for Fidelity National Information Services Inc., said a person with knowledge of the matter.

The offer would value Fidelity, a Jacksonville, Fla., payment-processing company, at about $32 a share, the person said, speaking on condition of anonymity because the discussions are private. An agreement could be reached as soon as May 16 if talks do not collapse, the person said.

A $15 billion deal would be about three times as big as the largest leveraged buyout since the credit markets crumbled in July 2007, showing how private-equity firms are again putting capital to work after a more than two-year drought in transactions. Other private-equity firms have recently held talks about joining the group bidding for Fidelity, said two people with knowledge of the matter.