"For Khvicha, playing against Real Madrid was special," he told Georgian football outlet Geo Team.
"He has always dreamed and I am convinced that he still dreams of playing for Real Madrid.
"In my family, everyone is a fan of Los Blancos - except for me. For this reason it was a very special match."
Kvaratskhelia burst onto the scene with Napoli as part of their Serie A title triumph last season, and has continued his good form despite the team's decline in 2023-24.
Reports suggest Chelsea are monitoring the attacker along with the likes of Manchester City, Newcastle and Real Madrid ahead of the January window opening in just a few weeks.
However, Napoli are said to want in excess of £86million with Kvaratskhelia under contract to 2027.
Partenopei teammate Victor Osimhen is another player interesting Chelsea as the winter market approaches, although scoring goals has been less of an issue for Mauricio Pochettino's side in recent weeks than keeping them out.