The film, directed by Thomas Vinterberg, recently won the Oscar for Best International Feature Film.
The sale of its English-language remake rights was reported by US media Deadline and has also been confirmed by Vinterberg.
According to Deadline, DiCaprio himself could play the role taken by Mads Mikkelsen in the original film.
Appian Way, a company co-owned by DiCaprio, successfully bid for the rights in partnership with two other companies, Endeavor Content and Makeready, according to the report.
Vinterberg told Danish newspaper Ekstra Bladet that the prospect of seeing DiCaprio in a headline role in the remake is “exciting”.
“(DiCaprio) is – as well as being the biggest and almost the only true movie star in the world – an absolutely wonderful actor, and I think his career choices show real integrity and talent. So I think it will be exciting to see what they can get out of it,” he said.
The Danish director does not expect to be involved in the remake, according to the report.
‘Another Round’ was on Sunday awarded the Oscar for Best International Feature Film.