Griezmann's contract will see his buyout clause set to €100m at the end of this season - with Barcelona expected to step in and trigger the option.
And at today's market rates, Lizarazu believes Atletico face missing out on millions.
He told Telefoot: "€100m is nothing for a great player. It's just a leg. He would be perfectly compatible with Barça. It would make an offensive armada.
"(Lionel) Messi likes to have a player in combination. With (Luis) Suarez, Griezmann could play around him. He has this collective game which suits the game of Barça. It would be an interesting career change."