Cooper, 65, has worked at GQ for more than 20 years and is seen as a legend in the US magazine publishing world.
However, the urbane title, with a focus on style and good journalism, has been suffering as low-brow lads' magazines such as Maxim have taken the US by storm. Maxim has a circulation of over 2m and Emap's FHM is over 1m, while GQ sells around 800,000.
Cooper was inducted into the Magazine Editors' Hall of Fame in January, prompting rumours that he was about to retire from his post. However, there is debate as to whether he is leaving of his own free will, or if he has been pushed by executives at Conde Nast, which is headed by chairman Si Newhouse.
Also named as a possible contender to replace Cooper is Dave Zinczenko, editor-in-chief of Men's Health in the US, a magazine that has recorded a 14% rise in circulation over the past year to sell around 1.7m copies. According to a report in the New York Times, an executive at Conde Nast said: "I think they will be casting a wide net, both domestically and internationally."
Cooper is reported to be finishing a semi-autobiographical novel on life at Conde Nast. He is to leave the magazine in June, just two months before his 20-year anniversary at the publication.
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