Big things were expected of the World Cup winner when he arrived at Camp Nou over the summer at the end of a protracted transfer saga.
It was expected that a proven performer well versed in the demands of life in La Liga would slot seamlessly into the Blaugrana fold alongside the likes of Lionel Messi and Luis Suarez.
Saul, though, has no doubts that a man with only three goals to his name so far will come good, telling Sport: “A player of his level can succeed anywhere.
“He has to feel comfortable, important, happy, the only thing he's after is enjoying football and if he's not enjoying the position he's playing or whatever, he won't be at his best. He doesn't just contribute on the pitch, at least not at Atletico. He's happy, positive. He's one of the players that is always good to have.”
It has been suggested that part of the problem Griezmann faces at Barca is being shoehorned into a position which may not be his best, but again Saul expects the 28-year-old to overcome those challenges.
He added: “Everyone will look for the best solution. He works hard, does his best for the team and if the coach decides if he should play on the left, he will do, and he will adapt to be one of the best on the left flank. He's really good, he always sacrifices himself for the good of the team and I only have super positive things to say about Antoine.”
On adapting to new surroundings, Saul went on to say: “It happens at all teams. You don't know the mechanisms, your team-mates, if a player wants it to feet or in space... they're details that come in time. You can be happier because of the weather, the city, the family, but at the end of the day these are the things you have to adjust to and [Griezmann] will be more and more happy in Barcelona all the time.”
With Griezmann no longer in the Spanish capital, Atletico had to move to bring in a suitable successor in the last transfer window.
Portuguese starlet Joao Felix was the man they turned to, with Saul impressed by a teenage forward snapped up for €126 million ((£113m/$142m) from Benfica.
The Spain international said: “He has something different. Don't forget he's only 18, very young, but he's won me over with his desire to learn, to improve, to learn and to contribute to the team. He's adapting still and when he's 100 per cent, you can demand more. Now he's giving everything on the pitch, doing well for the team. Every time he gets the ball, he looks to the goal. He's one of those different players.”
Felix was one of a number of new arrivals at Wanda Metropolitano over the summer, with Hector Herrera and Kieran Trippier among the other fresh faces.
Saul added to La Liga’s official website on the Rojiblancos new boys: “The two full-backs Renan Lodi and Kieran Trippier, they’re great at getting up and down the wing, they’re top players and they pose a real threat because they’re excellent at crossing. They’re also adept at coming in from the flanks, so I think they’re real all-rounders.
“As for Felipe and Mario Hermoso, both of them are very experienced and top class centre-backs, but their most salient and important feature – as with the rest of the signings – is that they have a willingness to learn and to listen, regardless of how experienced they may be. I think it’s very positive that they’ve settled into the squad very well, as from the very first moment they’ve tried to adapt to things here.
“Last but not least, there’s [Ivan] Saponjic and Joao Felix. Joao Felix is getting more playing time than Saponjic, but the same goes for him as the other lads – he’s always working hard in training, he’s a very strong guy when it comes to holding off defenders and creating space, and he has great movement in the box.
“I think we've signed players across the whole pitch, who aside from being talented footballers are great people who bring a lot to the dressing room. This is especially important given that over the summer a lot of veterans who were important to the squad moved on.”