The Sun claim he will reunite with fellow Spaniard Unai Emery at The Emirates, three years after the pair worked together at Sevilla.
Monchi spent almost 20 years at the Spanish club, bringing in the players that would lead them to promotion from the Segunda Division and later five Europa Leagues and two Copa del Rey trophies.
In doing so, he has proved himself one of the shrewdest operators in the business and Gunners fans will be the first to tell you they could do with a sprinkling of his magic.
Here, Express Sport explores Monchi’s greatest triumphs.
Monchi to Arsenal: The ex-Roma transfer guru has worked his magic in the past
Monchi signed Dani Alves for Sevilla in 2002 for just £1million
With a whopping 38 trophies (and counting) to his name, Alves is the most decorated footballer in the history of the game.
His first in Europe came at Sevilla in 2006 when they won the UEFA Cup, four years after moving to the club from Bahia in Brazil for – yes really – £1million.
As Alves carved out a reputation as the best attacking full-back in La Liga, Barcelona became the natural next step and they were more than happy to pay £30million to get him.
He spent eight years as Barca’s first-choice right-back before moving on to Juventus and then Paris Saint-Germain.
At 35, the Brazilian is not getting any younger but he shows no signs of slowing up. He has even looked comfortable when required to cover in midfield at PSG.
Alves has previously said he would like a crack at the Premier League. Worth a punt, Arsenal fans?
Ivan Rakitic left Sevilla for Barcelona in 2014
Sevilla signed the Croatian midfielder from Schalke under Monchi’s guidance for less than £2million on the final day of the January transfer window in 2011.
He proved an immediate bargain with six goals in the second half of the 2010-11 campaign before becoming the focal point in a team that lifted their first of three Europa League trophies in a row in 2013-14.
Unsurprisingly, Rakitic moved on after that season but not before Sevilla turned a tidy profit.
Barcelona came calling and paid Sevilla around £14m to take him to the Camp Nou.
Since moving to Barca, Rakitic has become a three-time La Liga winner, won four Copa del Reys, the Champions League, the UEFA Super Cup and the Club World Cup. Oh, and he also played in the World Cup final last year.
Nicolo Zaniolo was one of Monchi’s best signings at Roma
Probably Monchi’s biggest success story from his time at Roma.
Zaniolo moved to the Stadio Olimpico as part of the deal that saw Radja Nainggolan move to Inter Milan.
When Inter agreed to pay £20m plus Zaniolo and Davide Santon, many Roma fans were furious at losing a player who had been a key figure for two who were supposedly below his level.
However, it proved to be a masterstroke by Monchi. Nainggolan has faded badly and is still struggling to settle at Inter, while Zaniolo is now rated as one of the most promising youngsters in Italy.
The midfielder, 19, scored twice on his Champions League debut against Porto to become the youngest Italian to net a brace in Europe’s premier competition.
Carlos Bacca won the Europa League twice at Sevilla
Another Monchi bargain, Bacca won the Europa League in both of his two seasons at Sevilla, scoring 49 goals in 108 appearances along the way.
The Colombian cost the club £5m in 2013 and was sold to AC Milan for £26m two years later once his best years were behind him.
Bacca started well in Milan but failed to replicate the kind of form that had made him such a lethal force in La Liga.
Barca returned to Spain with Villarreal in 2017 and had an excellent first season. However, he is now scoring at a rate of just 0.26 goals per game.
Monchi has left Roma and is reported to be close to joining Arsenal
According to the Sun, Monchi could well be announced as Arsenal’s new director soon.
Arsenal have endured two frustrating transfer windows, where fans were expecting the club to spend big money.
But the heavy investments in Pierre-Emerick Aubameyang and Alexandre Lacazette over the past 13 months has been a sign of their transfer progress under Emery.
Gunners fans were left frustrated for years under ex-manager Arsene Wenger, who stood by the company line of not splashing the cash too much.
No doubt the Arsenal board will be hoping Monchi brings some of his transfer magic to north London.
Monchi to Arsenal: The transfer guru is free to join the Gunners
Monchi himself has responded to the speculation, saying: “I do not want to talk about it.
“I always want to stay with positive thinking, that is, having had the chance to have worked in Rome with Roma.
“I do not think it’s time to examine these things. It’s time to remember beautiful things.”