Fabregas has been linked with moves to Barcelona and Real Madrid in recent weeks.
“I can’t marry the stories that I read with the reality, which is that Cesc is extremely happy at Arsenal and totally committed to the club, and that’s every message that Arsene Wenger or I have ever received from him or his representatives,” said Gazidis.
“I am very confident that Cesc is committed to the club.
“You never relax about any situation but we are very confident that this team will stay together, progress together and achieve success together.
“The young players that we have and the manager we have believe we are doing something very special here.
“Arsenal offers good money, it offers a great development programme, a superb environment so it is difficult for me to imagine why players would want to leave.
“I can’t guarantee success because success depends on those very players but am I confident that I can keep those players and we can make progress? Absolutely, very confident.
“It’s not good enough for us to be in fourth place, we have to be competing for the Premier League title.
“I think there are a variety of reasons we are in fourth place but it’s not the level of our ambition – not the level of Arsene Wenger’s, the board’s or my ambition.
“Arsene believes he is developing a superb team of young players who can compete for the Premiership for many years to come.”