Ramsey whose contract expires at the end of the season looked set to extend his stay with a new deal.
Explaining his own exit earlier this month, Gazidis - who was instrumental in the appointment of Emery - said: "I know many will think this is a odd time to be leaving but I believe it is the right time for me and for the club".
Unai Emery saluted the patience of Bernd Leno and challenged the German goalkeeper to seize his chance after an injury to Petr Cech. I am happy because we are becoming more competitive. 'I spoke with him, because the most important thing was that he was prepared when the team needed his help. This situation, in the pre-season and now, is the same.
The Arsenal boss has remained tight-lipped on the midfielder's situation with the club, with Emery offering up a convoluted response when pressed on Ramsey's situation and if he wanted to keep the Wales star around . Alexis Sanchez moved to Manchester United in January after refusing to sign a new deal, while Mesut Ozil finally penned a new contract that same month worth upwards of £300,000 a week.
Ramsey is Arsenal's longest-serving player and Emery talked openly during preseason about the importance of signing him to a new long-term deal, saying he viewed the midfielder as a key part of his team. But Emery also appeared to suggest he understood every player had to maximise his earning potential during what is a short career. "We had a very good performance with more shots, more shots on target, a lot of clear chances to score".