Griezmann has publicly declared he wants his future to be decided before the World Cup in Russian Federation, with the 27-year-old set for a big summer as part of a talented French side.
Barca's apparent pursuit of Griezmann prompted Atletico to complain to Federation Internationale de Football Association over improper conduct in December, though the Camp Nou side denied their claims.
Neymar left Barcelona for Paris Saint-Germain last summer and has been linked with a move to Real in the future.
Griezman has been linked with Barcelona after another splendid season with Atletico, scoring 27 goals in all competitions.
"[Griezmann] has been playing at the top level for many years, fighting for everything".
Second-placed Atletico trail leaders Barca by 12 points in La Liga and while that gap can be cut to nine if they beat Real Sociedad on Thursday, it would take a stunning collapse for the Catalans not to be crowned champions. He leads Atletico's attack, which is fundamental [in showing his quality]. "He will be welcomed".
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Barcelona have enjoyed a superb 2017-18 campaign, winning La Liga and the Copa del Rey.
Atletico, who are now second in the league, face Marseille in their third Europa League final in eight years in Lyon on 16 May after beating Arsenal in the semi-finals.
"We have to give our team all the tools so that when a player has to decide, they will want to continue with us".
"It's an embarrassment, the players have to show our faces, we all make mistakes", Alba said of the Champions League exit. "He's managed the dressing room perfectly".
However, he has failed to earn a regular place in Ernesto Valverde's side despite showing improvement, and Bartomeu added: "That's the manager's decision".