There has been a host of speculation surrounding the Argentine's future this season, with some reports earlier this year claiming that he had made the decision to leave Wanda Metropolitano.
According to Marca, Simeone was presented with a 'dizzying offer' by Al-Ahli to become their new manager, with the club identifying the 53-year-old as their leading target in the dugout.
However, the experienced head coach has allegedly made it clear that he is not prepared to leave Atletico this summer despite a difficult 2022-23 campaign.
ESPN reports that Simeone is not interested in 'abandoning his job' in the Spanish capital, as he attempts to make the Red and Whites La Liga title challengers next season.
Atletico finished bottom of their Champions League group last season, which meant that there was no European football at Wanda Metropolitano in the second half of the campaign.
However, the capital outfit were largely impressive in the league after the break, ultimately finishing third in the table, just one point behind second-placed Real Madrid.
Atletico have already boosted their squad this summer with the arrivals of Javi Galan, Caglar Soyuncu and Cesar Azpilicueta, and more signings are expected before the end of the window.
Simeone has a contract with the Red and Whites until the end of next season, and Atletico president Enrique Cerezo said that the head coach would remain at the club "until the day he wants to leave".
The South American has been the head coach of Atletico since December 2011, taking charge of 627 matches in all competitions, boasting a record of 369 wins, 145 draws and 113 defeats.
Simeone is the longest-serving manager in La Liga, while he has won two La Liga titles, one Copa del Rey, the Spanish Super Cup, two Europa League titles and two UEFA Super Cups since arriving at Atletico.
The head coach has also led the club to two Champions League finals during a successful spell, and he will be looking to improve on the team's poor European performance in 2022-23 next season.
Alvaro Morata is currently being heavily linked with a move away from Atletico, with AC Milan said to be interested, while a number of Saudi Arabian clubs are thought to be in the hunt for his services.