The Irish actor starred as Agent 007 from 1995 to 2002

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Pierce Brosnan is very used to being asked his opinion on who should take over as James Bond after his successor, Daniel Craig.

"Sometimes it becomes wearisome," he admits to PEOPLE.

Still, Brosnan, 68, whose new film False Positive is now streaming on Hulu, understands why fans are interested in hearing what he has to say.

"You have to get over that and celebrate it as a member of the audience and as a man who has kind of walked that walk and played that part," he continues. "Bond will live on here."

From 1995 to 2002, Brosnan played Agent 007 across four films: GoldenEye, Tomorrow Never Dies, The World Is Not Enough and Die Another Day. Brosnan - who stepped into the role after Timothy Dalton - was succeeded by Craig. 

Pierce Brosnan
Credit: Matt Winkelmeyer/Getty

Craig, 53, announced in November 2019 that No Time to Die will be his last time playing the beloved English spy.

"Daniel was magnificent and he can walk away head up, shoulders back. He truly left an indelible mark on the franchise," Brosnan says of Craig. "My time and years of doing it, a decade, was one to be cherished and one that is a gift that keeps giving, having played that role."

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No Time to Die
Daniel Craig as James Bond
| Credit: Universal Pictures UK/Youtube
Pierce Brosnan
Credit: MGM/ Everett

Brosnan admits that he has "no idea" who should tackle the coveted part next, but there are two actors that he believes would be a good fit.

"Idris Elba comes to mind," the Irish actor says. "Idris is such a powerful presence and such a great former voice tensity. He would be magnificent. There's Tom Hardy out there as well. Tom can really chew the furniture up, just be a ball boy - both men can."

He adds, "And I think now that Daniel has left such an indelible footprint, they can go in many different ways. But your guess is as good as mine, who's going to be the next Bond. There's no other franchise like it. Nothing."

Fast Positive follows married couple Lucy (Ilana Glazer) and Adrian (Justin Theroux) as they seek Dr. Hindle's (Brosnan) assistance in helping them to conceive a child. However, over time, Lucy begins to notice that something is not quite right with Dr. Hindle and works to unravel the truth from there.

False Positive Pierce Brosnan
Pierce Brosnan
| Credit: Hulu

"It's an homage, in some way, to Rosemary's Baby," Brosnan teases of the film. "It has a similar tonality."

John Lee and Glazer's writing was something that attracted Brosnan to the project, as he believed that "it could possibly throw a spotlight on part of our society that exists."

"A24 has found a wonderful kind of position for themselves with movies like Midsommar and Hereditary. So I was very excited to work with that company," he also says of A24, which produced the film for Hulu. "I've been watching them for some time now deliver great works and great performances and storytelling and doing it on a strict budget."

False Positive premieres on Hulu on June 25.