Mikel Arteta and Julian Nagelsmann have emerged as the front-runners for the Arsenal manager's job, Sky Sports News understands.
Arteta, currently Pep Guardiola's assistant at Manchester City, and Hoffenheim manager Nagelsmann head the queue after Juventus manager Massimiliano Allegri said he would be staying at Juventus unless he was sacked.
As things stand, it is understood Arsenal have not made an official approach yet for club legends Patrick Vieira or Thierry Henry.
Former Barcelona manager Luis Enrique is reportedly interested in succeeding Arsene Wenger at the Emirates, but his wage demands are putting Arsenal off.
The club are expected to begin the interview process this week in the hope a new manager will be in place before the start of the World Cup on June 14.
Guardiola has said he will not stand in Arteta's way if Arsenal come calling but also said he would be "the happiest guy in the world" if he his fellow Spaniard stayed with Manchester City.