Arsenal are exploring their options after 68-year-old Arsene Wenger announced he would be leaving at the end of the season.
Simeone is a dark horse for the job with fans more obliged to appoint him than the management team.
Express Sport understands Luis Enrique is frontrunner for the Arsenal job, while Juventus’ Max Allegri has also been approached.
The Argentine is also in the frame for the Chelsea job.
The Blues are primed to axe Antonio Conte after the Italian’s constant criticism of the club board.
Conte has also overseen a difficult season at Chelsea with Champions League football for next term looking set to evade them.
Yet The Mirror say Simeone is not interested in either Arsenal or Chelsea jobs.
Instead, he would rather stick it out in La Liga and attempt to steer Atletico to a first league title since 2014.
However, pundit Gary Neville thinks Arsenal should do all they can to bring Simeone to the Premier League.
“I spoke about Diego Simeone as a candidate to replace Arsene Wenger in my podcast and the reaction I got on social media was that his style isn’t the Arsenal way,” Neville told Sky Sports.
“What I would say is Arsenal isn’t defined by Arsene Wenger.
“The last 10 years have been very different to the previous 10 years and if Arsenal feel the football they have to play is the ‘total football way’ then perhaps they’ll go for Luis Enrique.
“But Simeone is the outstanding candidate in terms of taking on rivals with bigger budgets.”
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