Umtiti arrived at Barcelona in the summer of 2016 from Lyon and has quickly established himself as a regular at the heart of the Catalans' defence.
That form has also seen him break into the France team, where alongside Griezmann the youngster helped Les Bleus clinch a place at the 2018 World Cup.
Now, with Griezmann's Atletico struggling to reach the heights of previous seasons, Umtiti believes he would be a fine addition to the Blaugrana squad.
"We have already seen what he can do at Atletico, he is a world-class player," the 23-year-old signalled in an interview with Ara.
"If the opportunity to sign him is there I will tell him not to hesitate, and to come to Barca."
The opening phase of Barcelona's Liga campaign has taken place in the shadow of constitutional crisis in Catalunya, with the region's parliament declaring independence and the national government led by Mariano Rajoy responding with the imposition of direct rule.
A controversial vote on separation was accompanied by scenes of violence in Barcelona, and Umtiti admitted that even as a foreigner he could not help but be affected by the upheaval - especially when Barca were forced to play a home game against Las Palmas behind closed doors due to the situation.
"[Gerard] Pique has explained to us what has been happening. He is a very intelligent person, a brave guy," he said.
"But after all that he is still focused. It was vital to win, even if other things were going on.
"It was strange but the only option open to us was to win. Life is like that sometimes. There was no need to convince Pique and Sergi Roberto, it was the president's decision to play and they understood. Everyone understood."
Umtiti also had warm words for Lionel Messi, who has been in spectacular form to lead Barca to the Liga summit and eight points clear of Real Madrid after the first 10 games.
"I don't want to think about having to defend against him at the World Cup," he joked.
"He is the best player in the world, he makes all the difference. Whether he wins titles or not, he is the best. There is no debate on that. He never lets you down."
Barca's bid to regain the Liga title from Madrid continues on Saturday, when they host Sevilla at Camp Nou.