“I am happy at Atletico and am close to renewing my contract,” he told Canal Plus France television.
“We are on track.”
He also revealed that he is not waiting for a call from fellow Frenchman Zinedine Zidane to play at Real.
“No, he hasn’t called me but I am good at Atleti,” he said.
“First he would have to call me and then I would tell him that I am happy here.
“He is a great person and a great player,” he added jokingly.
The Frenchman is looking forward to the European Championship in his home country.
“I am very pleased with everything that has happened to me in 2016.
“I hope we can crown it by winning in Milan and then Euro 2016, which will make me incredibly happy.
“This is going to be the first Champions League final for me and I hope to be lifting the cup.”I want to win the trophy and have a great game.”
Griezmann has been brilliant for Los Rojiblancos this season scoring 32 goals in 53 games, the most important being the one in Munich that sent Atletico to the Champions League final where they will meet city rivals Real on 28 May.
The striker has been heavily linked with a big money move to the Premier League this season, but it looks like that will not happen, which will make Diego Simeone extremely happy.