New York Liberty president Isiah Thomas said in a tweet on Thursday that he is not interested in becoming the Knicks' president.
Thomas was previously a "dark horse candidate" to replace Phil Jackson, according to Frank Isola of the Daily News.
The Knicks are also discussing Thunder GM Sam Presti as a replacement for Jackson, reports Ian Begley of ESPN.
Masai Ujiri, the president of basketball operations for the Raptors, is also being considered.
Thomas was named New York's President of Basketball Operations in December 2003, and kept the role until Donnie Walsh replaced him in April 2008.
Thomas also served as head coach of the Knicks during his final two years with the team from 2006-2008, leading New York to a 56-108 record.
Upon finishing his second season with a franchise record 59 losses, Walsh informed Thomas he would not be returning as head coach.