The Gunners are said to have spoken to Gilberto Silva, who has been asked if he wants the job.
Silva is another Brazilian former midfielder who played for the Gunners and won the Premier League.
Per The Mirror, Arsenal may be looking at Gilberto and other ex-players as options.
Gilberto told Sky Sports recently about Edu leaving Arsenal: "We exchanged a couple of messages, but I didn't ask him why he made the decision.
"Edu is a very cool guy. I think it was a tough decision for him to leave the club and I wish him the best of luck. He has done a great job for the club and, of course, I think the club will miss him. He made a great partnership with Mikel in order to have a good balance for Arsenal.
"Honestly, it was a big surprise for me but sometimes it happens and I hope that he'll be happy with the next challenge and whatever he decides to do."
Gilberto was then asked if he would be interested in replacing Edu and responded: "I still do some work with the club as an ambassador.
"This is not something I was (thinking about doing) in the next few years, despite the fact that I have done it for Panathanaikos in the past. In the last few years, I have been on a different road in football and with Arsenal.
"I don't know, I don't know. I have done the preparation for it a few years ago and I have been (approached) by a few clubs in Brazil, but I decided not to take the position. I am not saying right now, but it's always great to be around Arsenal even as an ambassador."