Griezmann's future is up in the air. The Frenchman refuses to rule out a possible Atlético exit and is rumoured to switch allegiances in the summer. He recently declared he wants his future in order before the World Cup.
Many have left since the turn of the Simeone era, but only one has triumphed elsewhere: Griezmann's current partner in crime, Diego Costa.
Whilst Costa had success with Chelsea in the Premier League before returning to the Spanish Capital, Filipe Luis, who followed the same path, did not. The full-back struggled to adapt at Stamford Bridge and was sent back to Madrid.
Nevertheless, it's Arda Turan who provides the clearest example of post-Atlético failure. Aspiring to lead Barcelona to glory alongside Lionel Messi, the Turkish winger blended into the scenery in Catalonia, and played just 55 times in two and a half seasons.
Radamel Falcao suffered a similair fate to Turan. After showing promise on the French Riviera with Monaco, Falcao underwent woeful loan spells at Manchester United and Chelsea showing himself as just a shell of the player that scored 70 goals in just 91 games for Atlético.
Jackson Martínez, a player who struggled to fit in in Madrid, scored just three goals before making the move to China. Unfortunately, he didn't shine with Guangzhou Evergrande either and now finds himself without a club.
One of the more recent examples is Theo Hernández, who made a controversial move to arch-enemy Real Madrid to contest Marcelo's place in the starting line-up. Needless to say things are yet to work out for Hernández who is still to win over Zidane.
With all these stories in mind, Griezmann will have to make a decision on his future at Atlético. Whilst the chance of joining a 'bigger club' is tempting, the Frenchman will fear following in the footsteps of those who left before him.