The 28-year-old announced his intention to leave Atletico at the end of the 2018-19 campaign and it has been suggested that he agreed on a switch to Camp Nou way back in March.
But while a deal has yet to be finalised, Lucas is interested in linking up with his compatriot again, believing a move to Bayern would suit him.
"[Griezmann] is a big player and many clubs would like him," Lucas told a news conference.
"Of course, it would be great to have him here, although I do not know if the club are interested in him.
"I do not know if Barcelona would be perfect for him, but if there was a chance he could come here, he might become the best player in the world."
Lucas, introduced as a Bayern player on Monday after completing a £68 million ($36m) move from Atletico earlier in the year, added: "Bayern are one of the biggest clubs in the world - and it will always be like that, everyone knows.
The World Cup winner is taking Bayern great Philipp Lahm's number 21 shirt and acknowledges the need for him to subsequently deliver.
Lahm won 21 trophies in 16 years at Bayern and was widely considered as one of the greatest defenders of his generation.
"That's a historic number," Lucas said. "A great former player like Philipp Lahm has worn it.
"Of course, it is an honour to be able to wear this number here and I will try to reward the club as much as possible."