The Italian champions are keen to keep hold of the likes of Victor Osimhen and Khvicha Kvaratskhelia, so selling Kim could help them stave off interest in their star forwards.
Napoli are set to part ways with defender Kim Min-jae but Manchester United would have to pay the sum of €60m (£53m).
The 26-year-old has been stellar for Napoli this season, helping them clinch the Serie A title last Thursday after he joined from Fenerbahce last summer for just €18m (£16m).
Min-Jae came in as a replacement for Kalilou Koulibaly who left the Serie A side for Chelsea last summer.
The South Korean could be moving to Old Trafford if the Red Devils are willing to pay £53m for his services.
Corriere dello Sport reports that Napoli are aware there is interest in Kim and will likely accept a hefty bid.
The Italian champions are keen to keep hold of the likes of Victor Osimhen and Khvicha Kvaratskhelia, so selling Kim could help them stave off interest in their star forwards.