Gabi said the 27-year-old's team-mates had already tried to convince Griezmann to stay and he hopes the trophy helps.
"We already told him a couple of things... he can't leave us," he told reporters.
"Let's hope today's performance convinces him to stay there."
Asked if Griezmann – who refused to discuss his future after the win – was thinking about his decision, Gabi said: "Yes, of course.
"Otherwise he would be in another team now."
Griezmann has scored 29 goals this season, with the Europa League crown his second trophy at Atletico since arriving from Real Sociedad in 2014.