Griffin turned down the opportunity because he and the Knicks couldn't agree on a role, a source said.
He and the Knicks "just couldn't make it work," a source with knowledge of the talks told ESPN's Dave McMenamin. The issue came down to finding a proper role for Griffin while front-office executive Steve Mills continues to work for the team.
With Griffin having withdrawn from consideration, sources with knowledge of the Knicks thinking said Mills will continue to lead the Knicks' front office for the foreseeable future, as he has throughout free agency.
Sources told ESPN's Adrian Wojnarowski that the Knicks and Griffin were at odds over Griffin not having full authority on basketball decisions and over Griffin's preference to bring in his own staff. No formal contract offer was made.
Much of the Knicks' front office has survived several unsuccessful regimes, and the organization has been hesitant to make sweeping changes to the group, league sources said.
Griffin has been in New York since Friday's meeting with the Knicks, who are looking to bolster their front office following Phil Jackson's departure as president of basketball operations.
In his next job, Griffin is searching for autonomy in the front office and an ability to build a working partnership with the owner, according to Wojnarowski.
Griffin is expected to serve as a television analyst next season, and it's believed he has no other NBA job opportunities at the moment.
Griffin has a trusted inner circle of front-office and scouting personnel who played a part in building the Cavaliers' roster into one that went to three consecutive NBA Finals and won the 2016 championship.
Griffin spent three years as the Cavaliers' general manager, beginning in 2014, until his departure in late June. He was an assistant GM with the Cavaliers before then, going to Cleveland after rising from an intern to a top front-office executive over 17 years with the Phoenix Suns.
Since parting ways with Jackson, the Knicks, under Mills, made the decision to sign Atlanta Hawks guard Tim Hardaway Jr. to a four-year, $71 million contract, a move that has been met with shock inside and outside the organization. The Knicks have become a perennial lottery team, rife with organizational discord and dysfunction.
The club wants to make a commitment to going young, transforming the roster to players in the 25-and-younger range. New York says it wants to build around 7-foot-3 Kristaps Porzingisand continues to say it wants to move 10-time All-Star Carmelo Anthony in a trade. Anthony is willing to waive his no-trade clause for Houston and Cleveland now, league sources said, but there has yet to be a mechanism that allows those teams to give New York the young assets it wants for a trade.
ESPN's Ramona Shelburne contributed to this report.