As reported by Standard Sport, a lucrative offer is on the table already for Gazidis to trade England for Italy, but the Gunners are desperate to keep hold of their man, particularly as he is responsible for a wide variety of changes at the club over the past year.
I Rossoneri meanwhile are under new ownership yet again, with Gazidis identified early on as a potential candidate to take over as their Chief Executive.
The Gunners don't want to lose him though, as they see him as a vital part of the transition process following the departure of long serving manager Arsene Wenger. Former Paris Saint-Germain boss Unai Emery is now in the hotseat, but Gazidis is wanted to oversee the early part of his rein at the very least.
Gazidis and Wenger are believed to have clashed after a power shift saw the Frenchman's authority diminish as responsibilities were delegated in a wider spread. Emery isn't expected to wield half of the authority Wenger enjoyed for the majority of his years in charge given the executive's appointing of a number of backroom staff.
Arsenal now house nine new department chiefs. Gazidis, head of recruitment Sven Mislintat and head of football relations Raul Sanllehi are doing most of the decision making, while Emery is just required to coach and make recommendations. Majority owner Stan Kroenke does have the final say on most matters, however, Gazidis is responsible for a lot of the club's undertakings.
Milan's offer comes at a time when the chief executive is viewed as having completed his biggest tasks at Arsenal, yet it is understood that several senior heads at the club are urging him to stay.
As of Thursday, Gazidis was reported to be nearing a deal with Milan. However, no decision has been taken on that front as yet and the folks at Arsenal are presumably sweating over what has now become a great possibility.