Barca sealed a €120million move for Griezmann this month and is reportedly keen to bring Neymar back from Paris Saint-Germain, which signed him for a world record €222m in August 2017.
The World Cup winner is unwilling to contemplate lining up alongside the Brazilian until a deal is done, with the Catalan giant reportedly offering €100m and two of Ousmane Dembele, Philippe Coutinho, Samuel Umtiti, Nelson Semedo, Ivan Rakitic and Malcom in exchange.
Griezmann thinks it will be tricky for Barca to get a move over the line and stated it already has sufficient talent to challenge on multiple fronts.
"We have to get it done first, because it is a difficult transfer," he told Sky Sports. "But he is a great player, hes had a couple of injuries but is at an incredible level. We also have Dembele, Coutinho and Malcom who are also important players for us and lets hope we can achieve great things with them.
"I hope I will have an important role, I want to be an important player for the team and help in whatever way I can.
"As long as I enjoy playing with my team-mates and give it all on the pitch, it doesnt matter."
READ | Griezmann cried with happiness after joining Barca from Atletico
Messi hasnt called yet
The France international said he received a warm welcome from those present on the clubs tour to Japan, where it will play Chelsea and Vissel Kobe in the Rakuten Cup, despite being nutmegged twice in his first training session.
Luis Suarez and Lionel Messi are not present in Asia due to their Copa America commitments for Uruguay and Argentina respectively, but only the former has been in touch with him so far.
"The truth is it started badly because they nutmegged me twice in my first rondo. Luckily I have learned the lesson," Griezmann said at a news conference ahead of Tuesdays meeting with Chelsea.
"Messi has not called me yet, but Suarez did. He congratulated me and welcomed me.
"The group has welcomed me and I am happy to share a dressing room with them. Hopefully I can help in the best way possible."
READ | Playing next to him is an incredible joy - Griezmann ready to link with Messi
Atletico challenged the legitimacy of Griezmanns transfer to Barcelona, alleging the La Liga champion should have to pay the €200m release clause that was still active when they began discussions.
Griezmann would not be drawn on his former clubs complaint and stated his focus was on adapting to his new team.
"I did everything as well as possible with respect to Diego Simeone, my former team-mates and Atletico Madrid to leave on good terms," he said.
"Its an issue for them. I am calm and all that matters is starting well with Barcelona, which is the most important thing.
"I heard about it [the complaint]. Its a club where I gave my all. Im very calm. The only thing that matters to me right now is understanding the coachs tactics, getting on with my team-mates and enjoying football."
READ | Simeone grateful for Griezmanns faultless Atletico stint
On Simeone, he added: "Our relationship was more than a coach and a player, were like family. I got on very well with him.
"He was important for what I did on the pitch and for my private life. I owe him a lot and I love him a lot. Our relationship will carry on, even after retirement."