Enrique left his post at Barcelona after three successful years at the Nou Camp, where he won La Liga twice as well as the Champions League.
The Catalan giants have replaced him with former Athletic Bilbao boss Ernesto Valverde, who has enjoyed a fine start to to his time at the club.
But Spanish website Diario Gol say that Messi actually wanted the Barcelona job to go to Atletico’s Simeone instead.
Simeone is widely regarded as one of the best managers in world football, having turned Atletico into one of the most consistent clubs in Europe.
The Argentine masterminded their Europa League triumph in 2012, with the La Liga side following that up with the league title two years later.
And, though Real and Barcelona have since dominated Spain’s top flight, Simeone has stuck with the club through thick and thin.
Diario Gol say, however, that Messi was keen for him to be Enrique’s replacement.
The 30-year-old reportedly admires how Simeone is able to coax the best out of Atletico players despite having precious few resources.
But Simeone chose to stay at Atletico because he wanted to be part of a bright new era at the Wanda Metropolitano.
Additionally, Barcelona never even considered his appointment.
They supposedly deemed him ‘overrated’ despite all his achievements with Los Colchoneros.
And club chiefs also thought Messi was blinded by wanting a fellow Argentinean to take on the role.