The "Big Little Lies" actor was already a fan of the British author's other works when he was approached for the new project, and although he wasn't familiar with the storyline of the 1983 novel, he would have done anything to work with "Oldboy" writer/filmmaker Park Chan-wook, who makes his TV directing debut with the miniseries.
"I've read a couple of other John le Carre novels, but I had not read this one," Alexander told U.S. talk show "Live with Kelly and Ryan". "Park Chan-wook directed all six episodes, so I said yes (to the job) before reading it. He did the Old Boy trilogy, The Handmaiden; he's an extraordinary, extraordinary filmmaker, so it's one of the few times you basically don't have to read (the script), you're just like, 'Yes! I don't know what he wants me to do, but whatever it is, I'll do it'."
Skarsgard features alongside Michael Shannon and Florence Pugh in the new show, which debuts in the U.S. on Sunday night (November 18).
"The Little Drummer Girl", based in the Middle East in the late 1970s, stars Shannon as an Israeli spy, who is tasked with seeking out information about a young actress hired to kill a Palestinian terrorist. Skarsgard portrays his Israeli intelligence officer partner.
It's not the first time the book has been adapted for the screen. It was previously turned into a 1984 movie by filmmaker George Roy Hill, starring Diane Keaton, Yorgo Voyagis, and Klaus Kinski.