Messi became a free agent when his Barcelona contract expired on June 30, and planned to stay until the club announced that financial problems would prevent them from registering a new, agreed deal.
The 34-year-old eventually signed for Paris Saint-Germain on August 10, signing a two-year contract with the option of a further year.
"When what happened at Barcelona happened, we called Luis," Simeone told Argentinian newspape rDiario Ole on Tuesday. "I didn't call Leo. But I called Luis to say 'look, how is he? Would he be keen? Is there the slightest possibility... imagining that he could come to Atletico Madrid."
It lasted about three hours," he said. "Obviously Paris Saint-Germain were obsessed with that signing. The truth is that [coaching Messi] hasn't happened because he's been at Barcelona, we've been at Atletico, and while he's been with the national team I haven't been there."
The article has been sourced from ESPN.