The 24-year-old Frenchman has had a record-breaking first season in Madrid, finding the net 22 times.
     
Real Madrid star Ronaldo leads the tally with 39 goals while Barcelona talisman Messi follows with 38.
     
"I am focused on my work and my team. I don't think about others, only about getting better and better," Griezmann told during an interview.
     
The striker, who represented France in last year's FIFA World Cup in Brazil, wants to live up to the expectations of being the second most expensive signing in the Spanish club's history.
     
"I knew that people were expecting a lot from me due to having been the second most expensive signing of the club's history, so I have been trying to give back that trust on the field, to make the fans and my teammates happy.
     
"It's a different style of playing but I knew that I could do it. I am confident and I knew that everything was going to be all right if I worked hard."
     
Reigning Spanish League champions Atletico Madrid are currently third in the team standings behind Barcelona and Real Madrid, and Griezmann attributed the club's success in recent years to its Argentine coach Diego Simeone.
     
"I always say that I needed a coach like Simeone to progress. He encourages you non-stop, he gets the best of you because the player has no doubts in giving his all for him and the team.
     
"In every training session I learn something new thanks to him. The success of the team is largely due to his way of motivating the players. He is key," Griezmann, who had started his competitive career at Real Sociedad, said.
     
Even as English Premier league leaders Chelsea monitors Griezmann's situation at Atletico Madrid because of a buy-out clause of pound sterling 43 million, Simeone is adamant that the club do not sell its prize asset after just one season when he has a contract until 2020.
     
Even Bundesliga giants Bayern Munich recently showed interest in the French footballer.

Asked about the reported link-ups, Griezmann said, "Many things are published in the world of football. However, I am just thinking about Atletico de Madrid. I work everyday to improve and to achieve successes with my team. I just think about that."
     
Though he doesn't rule out a stint in England, Germany or may be Italy in the near future, Griezmann's priority right now is Atletico.
     
"To me there is nothing but the present. I only think about my team, about our next game, our next objectives. As I have already mentioned before, a lot of things are said in this industry. I can tell you that I play for a great club and I am very happy here."
     
Asked about Atletico Madrid club's immediate goals, he said, "The objectives of this club are centred on being competitive, so our most immediate major goal is thinking about our next match. We believe that the best way to go far is to focus on what's imminent and to compete.
     
"Let's see where we can go up to. But I'm convinced that with hard work and with the level of game we currently have, we can have a great season."
     
The young striker has scored more goals in one season than any Frenchman in La Liga's history. Griezmann scored his 22nd league goal at the weekend beating the likes of Zinedine Zidane and Thierry Henry and the previous record held by Karim Benzema in the 2010-11 campaign.
     
Griezmann is already 10th in an all time league table of Atletico Madrid strikers for goals in one season. He has beaten Fernando Torres's best ever haul of 19 in the 2006-07 campaign and is just five behind the 27 goals that Diego Costa scored last season.

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