Gazidis has been at Arsenal since 2008 and played a key role in bringing Emery to Emirates Stadium as a replacement for long-standing boss Arsene Wenger.
Milan’s recent takeover by Elliott Management, after former owner Li Yonghong failed to repay a €32million debt, has led to speculation new owner Paul Singer could move to appoint Gazidis.
But Emery, who is preparing his players for the new season at the International Champions Cup in Singapore, said his relationship with Gazidis remains strong.
He told reporters: “I speak every day with him [Gazidis].
“He has been committed here for many, many years. I think he continues here because it is a big project here and his commitment to Arsenal is very strong.
“We are speaking about every decision for our club.”
Arsenal – who have been busy in the transfer market ahead of the 2018-19 season, bringing in Stephan Lichtsteiner, Bernd Leno, Lucas Torreira and Matteo Guendouzi – released a statement in reaction to media stories about Gazidis’ future at the club.
“We are aware of the speculation surrounding our chief executive Ivan Gazidis,” the club statement read.
“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.”