Mike Marsland/WireImage; Kevork Djansezian/Getty
The two are in talks to embody the legendary Hollywood couple as the icons face a crisis that could end their careers and their marriage during the filming of their popular sitcom I Love Lucy, according to Deadline.
Sorkin (The West Wing) has written the screenplay and will direct the film, although it's unclear when production will start amid the COVID-19 pandemic.
I Love Lucy aired on CBS from 1951 to 1957 and spanned six seasons. Ball and Arnaz starred as married couple Lucy and Ricky Ricardo, as Lucy tries numerous schemes to be a part of showbusiness through Ricky's nightclub.
Archive Photos/Getty Desi Arnaz and Lucille Ball
The show also starred Vivian Vance and William Frawley, who played Lucy's best friends, Ethel and Fred Mertz.
Ball and Arnaz married in 1940 and had two children together: daughter Lucie Arnaz, 69, and son Desi Arnaz Jr., 67.
In 1950, Ball was starring on the radio with actor Richard Denning in the popular CBS show My Favorite Husband. When the network launched a version of the show for the new medium of television, she insisted that Arnaz, a nightclub bandleader, be cast as her spouse.
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While the show was a huge success, it took a toll on the couple's relationship.
Following 20 years of marriage, the pair divorced in 1960. "It got so bad that I thought it would be better for us not to be together," Ball said in court.
But they did find love again before their deaths (Ball died in 1989 and Arnaz in 1986). The actress enjoyed a fulfilling 28-year-marriage to comedian Gary Morton, and Arnaz retired, sold his share of Desilu Studios to Ball and married his neighbor, Edith Hirsch.
"I think she always loved him. And there's no question that he loved her always," I Love Lucy director William Asher told PEOPLE in 1991. "Later, he married her double. Edie [Mack Hirsch] was a marvelous girl in her own right, but she sure as hell looked like Lucy."