According to the Daily Mail, the production will be directed by David Leveaux - who was previously rumoured to be directing a revival starring Carey Mulligan - and "run at the Donmar from February for three months".
Marber's modern classic, set in London, centres on the tangled relationships between two couples: Alice, a young American stripper, and Dan (Chris), the writer who's penned a book about her experiences; and Larry (Sewell), a doctor, and Anna (Carroll), a photographer.
Closer premiered at the National in 1997 before transferring to the West End and, in 1999, to Broadway. In 2004, it was made into a film starring Brits Clive Owen and Jude Law and Americans Julia Roberts and Natalie Portman.
Oliver Chris is currently appearing in Great Britain, though the Mail reports he will not transfer with the production to the Theatre Royal Haymarket, and will instead rejoin the cast of King Charles III for its move to Wyndham's Theatre.
Rufus Sewell recently appeared in a West End revival of Pinter's Old Times, while Nancy Carroll's recent stage credits include The Magistrate at the National and The Recruiting Officer at the Donmar.