Emery, who left his job at PSG earlier this month, was in London on Monday for talks with the Gunners.
The 46-year-old Spaniard led the French Ligue 1 side to a domestic treble this season – but did not have his two-year contract extended and was replaced by Thomas Tuchel.
Former Arsenal midfielder Mikel Arteta was in the frame but withdrew from the process on Monday. He is understood to have wanted assurances over the role he will play in Arsenal’s transfer policy before agreeing to join the club as head coach.
The 36-year-old, who is a coach at Manchester City, also wanted guarantees that he will have a significant say in which players are to be sold to recoup funds for further investments, with the club’s summer budget reportedly at £50m.
Former Barcelona coach Luis Enrique is understood to have asked for similar guarantees during discussions with Arsenal.
Sky Sports Spanish football expert Guillem Balague told Sky Sports News on Monday: “I am hearing that Unai Emery is in London to hold talks with Arsenal. That has to do with the fact he is free, a top candidate and wants the job.
“We are talking about someone who has done such a great job in his career with the likes of Sevilla and only last week he was named manager of the year in France for the job that he did at PSG.”