Gase was believed to be the Browns' top target in their quest to replace Rob Chudzinski, fired after one season in Cleveland.
Last week, Haslam said the team is "prepared to wait as long as necessary" to hire a coach, and now the Browns will move ahead without Gase, who enjoys his role with the Broncos and may not be ready for a head coaching gig.
The Browns have interviewed at least eight known candidates to become their seventh full-time coach since 1999, and the team has set up second interviews with Seattle defensive coordinator Dan Quinn and Buffalo defensive coordinator Mike Pettine, the source said.
Quinn, who has presided over the NFL's top-rated defense this season, met with the Browns on Jan. 1 and reportedly impressed Haslam and CEO Joe Banner. Pettine had his first interview with the club on Jan. 16.
Per NFL rules, the Browns can conduct a second interview with Quinn by Jan. 26, but are not permitted to offer him a job until after the Super Bowl. Pettine can meet again with the team at any time.
Gase drew the Browns' attention and soared up their wish list of candidates helping quarterback Peyton Manning shatter several league records this season. Also, Haslam received a glowing recommendation on Gase from Manning, who has a long-standing relationship with the Haslam family because of their Tennessee ties.
Gase, too, fit the outline young, offensive-minded of the type of coach Banner wanted to bring to the Browns, who went 4-12 under Chudzinski and have lost at least 11 games in each of the past six seasons.
Gase is the second high-profile coach to remove his name from consideration. New England offensive coordinator Josh McDaniels also told the Browns he was not interested in pursuing their opening.
The Browns have also interviewed former Tennessee coach Mike Munchak and Dallas special teams coordinator Rich Bisaccia, who could both be brought back for second meetings.
AP NFL website: www.pro32.ap.org