Pettine was expected to visit the club for a third interview Thursday, said the person who spoke to The Associated Press on condition of anonymity because the team is not commenting during its search.
Unless there are unanticipated hang-ups, Pettine will become Cleveland's seventh full-time coach since 1999.
ESPN, citing multiple league sources, said the team is expected to offer Pettine the job.
The Browns have been looking for a coach since firing Rob Chudzinski on Dec. 29. Team officials flew to Mobile, Ala., this week to interview the 47-year-old Pettine, who spent one season with the Bills after four as defensive coordinator of the New York Jets.
Pettine is one of at least 10 known candidates to interview with the Browns, who dismissed Chudzinski hours after the season finale in Pittsburgh. The club had been expected to have a second interview with Seattle defensive coordinator Dan Quinn, who is preparing for the Super Bowl. But things have progressed to the point that the team is focused solely on Pettine.
AP NFL website: http://www.pro32.ap.org