Arsenal are "aware" of speculation around Ivan Gazidis' future but say their chief executive has rejected multiple offers in the past.
Gazidis is set to join AC Milan as executive director in September, according to Sky in Italy.
Sir Chips Keswick, Arsenal's chairman, did not deny Gazidis was the subject of an offer from the Italian club, but said his colleague has always been "fully committed" to the club.
"We are aware of the speculation surrounding our chief executive Ivan Gazidis," Keswick said in a club statement.
"We know he receives many offers from organisations inside and outside the game as he's a hugely respected figure. He has never accepted any of these opportunities and has never spoken about them publicly.
"He has always been fully committed to taking Arsenal forward and is currently working hard in Singapore with our new head coach Unai Emery as we prepare for the new season."
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Gazidis, who has been at the club for close to a decade, led the selection process which saw Emery appointed as Arsene Wenger's successor in May.
Emery's arrival was preceded by an overhauling of the club's structure by Gazidis as he brought in head of relations Raul Sanllehi from Barcelona and former Borussia Dortmund scout Sven Mislintat as head of recruitment.