Griezmann has been linked with a departure from the Madrid club for the last few years and will be available to rival clubs for €100m (£88.9m) in June when his buyout clause drops from €200m (£177.79m).
"All I ask of him is that as long as he is with us he keeps playing for his life," Gabi is quoted by Sky Sports News as saying after the game. "I just ask Griezmann that as long as he is here he defends this shirt like it deserves to be defended.
"I understand that not every player here has Atletico in their hearts and can change club and there's no need to criticise nor crucify them for that. Antoine is a special player for everyone, he's very much loved in the dressing room. He has a superior level of skill to the rest of the team and that's why he makes the difference.
"I've always tried to be close to him because he is a very important player for us. All I ask of him is that as long as he is with us he keeps playing for his life as he is doing at the moment and tries to make the difference, because he is one of the few players in the team that can do that."
According to reports in the Spanish media, Griezmann has already agreed to join Barcelona, with one radio station claiming that his partner has begun looking for homes in the city.