#4 Aaron Ramsey
Wenger recently confirmed that talks are ongoing with regards to Ramsey's contract extension. There were indications that many Premier League rivals including Chelsea and Liverpool are keen to sign the Welsh. As of now, nothing has quite materialized and Ramsey remains a key player in the team.
When the new manager takes over, it is expected that Ramsey will continue to have a role in Arsenal's midfield. Like Wilshere, Ramsey had suffered bouts of long injury spells. The player has made 31 appearances in all competitions this season and was given breaks in the early stages of Europa League and EFL Cup.
There is some sort of team balance when Ramsey plays with Granit Xhaka right in front of the backline. Ramsey, being the attacking minded player, enjoys making dangerous runs into his opponents' penalty box. That has allowed him to 11 goals in all competitions this season and provide another 11 more for his team-mates.
His importance for the team should not be overlooked by the incoming manager. It will be a priority for the Gunners to tie Ramsey down to a new long-term contract.