Griezmann was close to joining Manchester United before he dramatically chose to turn them down and pen a new contract with Atletico.
Simeone admits he spoke personally with Griezmann in the middle of negotiations.
The coach told Cadena Ser: "I spoke very clearly with him. He told me he would call me in a week and he explained what was going to happen.
"I was convinced he would not leave. I appreciate him very much."