The French international has been in scintillating form for Diego Simeone’s side this year, netting 22 times in 33 games.
Jose Mourinho is reportedly looking to bolster his side in preparation for an assault on next year’s Champions League.
Atletico are trying to tie the 24-year-old into a new deal at the Vicente Calderon, one that would raise his release clause to an astronomical £70m.
Griezmann has only been at Atletico for one year following his £24m switch from Real Sociedad, but recent performances have put him on Chelsea’s radar.
It is believed that the Frenchman has yet to decide whether he wants to stay at Madrid and Chelsea may be at the front of the queue.
Atletico fans will be on high alert following Chelsea’s raid on them last year, which saw them take Diego Costa and Felipe Luis to London.