The 50-year-old was reportedly offered the role of sporting director at the Emirates Stadium, shortly after he left the same post at Roma.
The former Sevilla goalkeeper decided to call time on his spell at the Stadio Olimpico after results had turned sour at the club in 2019, and he followed sacked Italian boss Eusebio Di Francesco out the door after a Champions League defeat against Porto.
Arsenal had reportedly tabled a three-year contract for the Spaniard and were said to be expecting him to start in his new role at the beginning of April, but he ultimately opted for a Sevilla homecoming.
Monchi explained his decision in front of the media on Monday, stating: "I appreciate the interest of Arsenal, perhaps the one that has shown the most interest, and of other clubs who have made contact.
"I have evaluated the proposals I had and I have chosen Sevilla.
"It was the one that brought things together and had the conditions for me."
It was claimed that Monchi was offered a £2.5 million per year package by Arsenal and they saw him as a crucial piece of the puzzle ahead of a restructuring of the club's hierarchy over the next few months.
The Gunners' loss is Sevilla's gain, as they welcome back a club legend who spent 17 years as their sporting director after a 10-year spell as a player at the Ramon Sanchez Pizjuan.
Arsenal must now go back to the drawing board in their hunt for a new head of recruitment, as they continue to target a place in the Premier League's top four.
Unai Emery's men will return to action after the international break, with a home clash against Newcastle scheduled on April 1.