Squid Game 's Lee Jung-jae on Season 2: 'Waiting for Director Hwang to Give Me the Whole Scenario'

CHRISTOPHE SIMON/AFP via Getty Lee Jung-Jae

Squid Game star Lee Jung-jae is excited for the show's second season — but he's also avoiding spoilers like the rest of us.

Speaking to PEOPLE about what he'd like to see in the series' sophomore run, Lee, 49, says, "I actually wanted to ask director [Hwang Dong-hyuk] about it too."

"But you know, when there's this present that you want... you're waiting for that [and] you're so excited to get it, you don't want to have it little by little," he explains. "You want the whole package at once, so I'm just waiting for director Hwang to give me the whole scenario, and I'm really excited for it."

While Lee was unable to reveal any specific details about the second season, he was able to disclose that Hwang is "diligently writing" the script right now.

"[It] looks like he has a lot of different ideas," he explains. "But writing a [script] is something that you don't know when it's going to [be finished]. Only director Hwang knows and [it] feels like he's really struggling to write the script."

Netflix Lee Jung-Jae

RELATED: Everything to Know About Squid Game Season 2

In Squid Game, Lee plays Seong Gi-hun, a cash-strapped gambling addict and father recruited to play a mysterious, deadly series of children's games in exchange for a prize worth millions. Season 1 ended (spoiler alert!) with Gi-hun seemingly ready to return to the arena he previously conquered in the name of revenge.

Lee previously told PEOPLE he'd like to see a season two plot that keeps the audience on its toes.

"I hope there's some sort of twist that'll be exciting and surprising for me and the viewers," Lee said in December. "If it was predictable, it would be no fun."

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While Squid Game allowed for Lee to be recognized worldwide, the actor has been a prominent talent in Korea for almost three decades. In 1995, he won multiple Best Actor accolades for his role in The Young Man and his 2013 film The Face Reader earned him a Best Supporting Actor award. And just last month, Lee made his directorial debut at Cannes with his film, The Hunt, a spy movie set in the 1980's.

In both acting and directing, Lee says gets his inspiration "from people."

"So, like this very moment, when I'm talking with a Squid Game fan, it's a source of inspiration for me. We might be from different countries. We might use different languages and we might have different cultures, but all human beings are just one species and we have this innate desire to know each other better," he says.

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The idea is something Lee believes has become even more clear over the years, especially with the rise of the internet and social media.

"I think the cultural barrier and the language barrier has been significantly lowered and Squid Game [has] made the worlds one," he explains. "Now, when we release a [Korean] song or a movie or a TV show, the whole globe watches at the same time, listens at the same time. I think we really live in a world without any silos now, and Korea and the states have long been cultural partners and economic partners. And I think it's just tighter and faster now, how the exchanges go and Korean people have always loved American media and content, and now it goes the other way too."

"The people in the states are curious about Korean culture and Korean content," he adds. "So I think this is just the beginning and I hope that we have more exchanges going forward."

Despite his new stardom, Lee says his life is pretty ordinary when he isn't accepting Screen Actors Guild Awards or walking the red carpet at the Cannes Film Festival.

"Actually, my life is really nothing special. What I do is I watch movies and I talk to the movie people about movies," he says. "Then, when I have some time, I write my scenario."

Season 1 of Squid Game is currently streaming in its entirety on Netflix.