The French striker has impressed at Atletico Madrid after making a £22m move from Real Sociedad in the summer.
Atletico have Griezmann tied to a deal until 2020 and are reluctant to renegotiate the terms of that contract due to his already-high wages, according to Spanish paper Mundo Deportivo.
But that could mean Chelsea - along with Bayern Munich and Paris Saint-Germain - might smell a bargain.
Griezmann's 22 goals in La Liga this season are the best ever by a French player in Spain and leave compatriot Karim Benzema trailing in his wake.
Last year Griezmann explained his reasons for snubbing Arsenal and PSG, saying: "Why Spain and not elsewhere? This is my championship, my home. I'm happy here.
"And Atletico is a great club. The leaders were willing to pay €30m (£24m) for me.
"I had the boss on the phone. He motivated me and said the club really wanted me. I knew that I was coming here to learn.
"Was it weird when PSG and Arsenal were also interested? They're still the champions of Spain!
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Antoine Griezmann is wanted by Chelsea
"I needed a club like that and a coach like Diego Simeone to progress.
"I always demands intensity in training. That's my style and I like it.
"The team captain (Gabi Fernandez) also called me to ask me to come and tell me I would feel comfortable here where there is a great family feeling in the changing room."
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