Barcelona's financial problems meant that they were unable to hand the experienced attacker a new contract, and Paris Saint-Germain swooped to land the South American on a free transfer.
Simeone has said that Atletico had hoped to use striker Luis Suarez, who is close friends with Messi, to set up a move to Wanda Metropolitano, but PSG were "obsessed with the signing".
"I'll tell you a detail," Simeone told Ole. "When what happened now at Barcelona happened, we called Luis (Suarez), with all due respect.
"I didn't call Leo, but I did call Luis, and I asked him to find out how he was, what he thought, if there was the slightest possibility, imagining that he could come to Atletico de Madrid.
"But that lasted three hours. Paris Saint-Germain were obviously obsessed with the signing. The truth is that we didn't have the chance to meet because he was always at Barcelona, and we were always at Atletico de Madrid, and neither were we at the national team."