The sale of the Carolina Panthers appears to be near.

David Tepper, the hedge-fund billionaire whom many N.F.L. owners pointed to as the preferred choice to buy the team, will not increase his offer to meet the current asking price of $2.5 billion, which makes it unlikely that he will win the ongoing auction for the club, according to two people with knowledge of his interest in the team.

Tepper’s decision comes a few weeks after Michael Rubin, the owner of the online retailing giant Fanatics, bowed out. Both men could return to the bargaining table if Richardson decided to accept a lower price.

Their apparent departures narrow the field to two for membership in the most exclusive and expensive owners club in North American sports: Ben Navarro, who owns Sherman Financial Group, an investment firm; and Alan Kestenbaum, the chief executive of Bedrock Industries, which owns and operates metal and mining companies.

According to several people familiar with the auction, Navarro is believed to have offered $2.6 billion, though it is unclear whether he needs the help of other investors to cover that price.