Simeone has guided Atletico to plenty of success since becoming manager in 2011 and leads them out in the Europa League final against Marseille tonight (7.45pm).
During his time with the club, Atletico have won La Liga and been runners-up in the Champions League on two occasions.
They last won the Europa League in 2012 with Simeone named European Coach of the Season that year.
And Griezmann believes the success the Argentinian is bringing to Atletico is similar to that which Ferguson had at United.
“What ‘el Cholo’ [Simeone] is doing for this club is historic,” Griezmann said.
“It reminds me a bit of Ferguson and what he did with Manchester United.
“Hopefully he’ll have that career because he deserves it, and he has taken the term where he intended, to the maximum, to among the best teams in the world. We are there thanks to him.”
Griezmann looks to have an unsettled summer with Barcelona reportedly pursuing the Frenchman.
The forward has a buyout clause of 100 million euros (£87.5m) but Barcelona may face competition from Manchester United.
And Griezmann praised Simeone for the way his game has improved in recent years.
“He has made me grow on a personal and professional level,” Griezmann added.
“I believe that tactically, on a defensive level he is the best in the world. You can see every year that it is a joy to be able to work with him.”