Little is known about the film, which is based on a screenplay written by Oscar winner Emma Thompson and Bryony Kimmings, other than it's a romance based in London and set around the holidays, according to The Hollywood Reporter.
Feig, who directed "Bridesmaids" and "Ghostbusters (2016)", will reteam with his "A Simple Favor" leading man Golding for the new movie. The filmmaker and Thompson are also set to produce "Last Christmas".
Clarke won rave reviews for her last movie romance, 2016's "Me Before You", while Golding made his feature film debut in this summer's "Crazy Rich Asians".
Meanwhile, Thompson is also writing and directing a stage musical adaptation of children's movie "Nanny McPhee".
The British actress wrote the screenplays and starred as the titular snaggle-toothed nanny, who transforms the lives of a widower and his seven troublesome children, in the 2005 movie of the same name and its 2010 sequel, "Nanny McPhee Returns".
She has now written a script for a stage musical adaptation, which she is both "excited and naturally nervous" about directing. She also told Britain's Daily Mail newspaper she is currently writing lyrics for the musical numbers alongside Scottish singer/songwriter Gary Clark, best known for his work on musical film "Sing Street", who is composing the score.
The "Love Actually" star won't be reprising the character onstage.
The production, which looks set for London's West End, is expected to go into rehearsals next year.
Emma is a seasoned writer, winning an Oscar for Best Adapted Screenplay in 1996 for "Sense and Sensibility", in which she also starred. In March, it was reported that the actress, who also wrote films "Effie Gray" and "Bridget Jones's Baby", was developing a script of "Harrow Valley" for the small screen. The original script for the period horror thriller was written by the now-deceased Walter Newman in the 1960s but never saw the light of the day.