United manager Erik ten Hag wants to strengthen his defence, with South Korea international Kim having been identified as his key target. Newcastle are also interested in the 26-year-old.
According to Calciomercato, Napoli want to sign Atalanta’s Giorgio Scalvini to replace him.
Kim was part of the Napoli side that won the Serie A title for the first time since 1990.
United can call upon the likes of Raphael Varane, Lisandro Martinez, Victor Lindelof and Harry Maguire at centre-back, but Kim would provide them with another option.
Kim impressed during his first season at Napoli following his move from Fenerbahce last year.
It is likely to be a busy summer at Old Trafford, with United also reportedly preparing a £50million bid for Chelsea midfielder Mason Mount.
United are interested in Harry Kane but face significant competition for the Tottenham striker, especially from Real Madrid.
During ten Hag’s first season in charge United won the Carabao Cup but they were beaten by rivals Manchester City in Saturday’s FA Cup final.