His worldwide team-mate Umtiti - who signed a five-year deal with Barca on Monday - said Griezmann would be a welcome recruit at Camp Nou.
Upfront, Lionel Messi is deployed as the support striker, meaning Griezmann could likely be played on the right before he eventually replaces Suarez when he moves on after a few years.
French publication Foot 365has claimed thatArsenal are due to meet with the player's representatives this week over a potential move to the Emirates.
Messi was asked about the speculation and admitted the world's best footballers will always be welcome at Barcelona; he also said he believes he would link up well with the France worldwide on the field, per Mundo Deportivo (h/t Goal).
"He is a great player and could help any team in the world".
"It's not yet one hundred percent, but the more quality we have, the better".
The 27-year-old forward - a Europa League victor with Atletico in 2017-18 after scoring 29 goals in all competitions - has a reported €100million release clause.
Fellaini, named in the Belgium squad for the FIFA World Cup 2018, sees his current Manchester United contract running out by the end of the season, and although manager Jose Mourinho wants him to stay, the midfielder has made his mind of moving away from the club.
Griezmann and Messi are both now preparing for the World Cup with their respective national sides, with France set to face the United States in their final warm-up friendly in Lyon on Saturday evening and Argentina having cancelled a proposed fixture against Israel in Jerusalem amid political pressure.
His and France's World Cup campaign will begin when Les Bleus face Australia on 16th June.