Messi ended a 21-year association with Barcelona in August after the Catalan giants failed to put a suitable financial package together to retain the six-time Ballon d’or winner.
The 34-year-old subsequently moved to the French capital on a free transfer, signing a two-year contract.
Messi and Suarez are good friends dating back to their time together at Barcelona, and Simeone tried to take advantage of that budding relationship to make a surprise swoop for his compatriot.
“I didn’t call Leo, but I did call Luis, to ask him how Messi was doing, whether he fancied it and whether there was the slightest chance of him coming to Atlético,” Simeone said to Ole.
"It was something that lasted three hours, because PSG already had their hearts set on signing him.
“So the chance to work with Messi has never come up. He was always at Barca [before joining PSG], I’ve been at Atletico and we didn’t coincide as players in the Argentina national team."
"If you ask me where Messi has to play, I’ll say in a team that wants to win," he added.
"In a team that knows what it needs to do to win. It doesn’t matter what position he plays; what matters is that the team is set up to win.
"Don’t think about him, think about the team."
Asked if he had any direct contact with Messi, Simeone said: "No, nothing at all; it was like watching a plane go by in the sky."
