Konsa is regarded as one of the best centre-backs in the Football League, with the 20-year-old having already made 62 appearances for Charlton.
The youngster was also part of the England squad which won the Under-20 World Cup earlier this year and according to the Liverpool Echo, his development is not going unnoticed by the Toffees.
Konsa was allegedly watched by the Premier League side when Charlton faced Blackburn Rovers at the weekend, with the player featuring for the full 90 minutes as the Addicks succumbed to a 2-0 defeat at Ewood Park.
Should Everton up their interest in Konsa, other top-flight clubs will likely make offers to rival the Merseyside outfit.
Konsa still has two-and-a-half years remaining on his contract at The Valley.