Arsenal have reportedly not contacted any of their preferred managerial candidates as they want to show respect to the clubs they are currently working for.
1Repect

Arsenal are hoping to announce their new manager before the World Cup on June 14.
Jeremy Wilson, writing in today’s Daily Telegraph, says the club have whittled their long list down to three preferred candidates, but they are waiting until the season wraps up across Europe before contacting any of them.
The club expect to move quickly once the main business of football is over.
“Arsenal,” he writes, “do not want to contact managers at an inconvenient moment and so will wait until most of the major European leagues have finished before accelerating their process.”

Wilson also reports that Arsenal have still not decided between an established manager and an up-and-coming, inexperienced one
When Arsene Wenegr announced that he was leaving Arsenal at the end of the season, David Ornstein said that the club had a short-list of five to replace the Frenchman. Three of those now remain as preferred candidates.
In the intervening weeks, this list grew quite spectacularly, but thankfully many of the fringe candidates who were awful choices have dropped away.
Gazidis also reportedly met with three managers before Wenger made his announcement. None of those three have made the short short list.
See Arsenal’s preferred trio next…