Ritchie and Wigram have a production deal at the studio beginning in January.
Warner Bros. has wanted to make a movie based on the 1960s television series for nearly 20 years, and a number of high-profile directors, including Quentin Tarantino, Matthew Vaughn ("X-Men: First Class") and David Dobkin, have been tied to it.
Ritchie directed the studio's 2009 hit "Sherlock Holmes" and its sequel, this month's "Sherlock Holmes: A Game of Shadows."
If he and Wigram take on "U.N.C.L.E.," they'll begin their deal at Warner Bros. with a high-profile project.
Deadline first reported the news.