Griezmann has been heavily linked with a move away from Atletico for two straight summers, with talk of a move to Manchester United in 2017 being followed by reports of a switch to La Liga champions Barca this year.
The Madrid club confirmed Griezmann had signed a new five-year contract at the Wanda Metropolitano.
Atletico Madrid officials were sent to meet the France players in Russian Federation. He would have been in the shadow of some great players like Messi, Iniesta or even Xavi before.
However, the 22-year-old looks set to join the Europa League winners in a deal reportedly worth £62.2million, pending a medical and finalising a formal agreement with Monaco.
Left-back Lucas Hernandez has also extended his contract at Atletico, with his now expiring in 2024.
Pique previously defended his actions, but he and Umtiti will have to answer to Barcelona when they return from World Cup duty with Spain and France respectively. He made the best choice for him and for his career. France's next match is against Peru on Thursday.