"If he wants to, he should go," Sagnol said after Georgia's defeat to Spain ended their participation at the tournament in Germany where Kvaratskhelia, nicknamed 'Kvara-dona' by fans, after Diego Maradona, has shone.
"If it's Napoli or Paris or whatever, I just want him to be happy and to still play with a lot of emotions because that is how he gets so fantastic.
"I just wish him all the best in his career."
Kvaratskhelia helped Napoli to the Serie A title in the 2022/2023 season - their first since Maradona played for them - winning both Most Valuable Player and Goal of the Season.
At the Euros, he tormented defences and scored in a shock win over Portugal that took Georgia past the group stage at their first major international football tournament despite being the lowest-ranked team.
That, inevitably, revived questions over his future, with some media reports saying he is weighing a contract renewal with Napoli versus interest from French champions PSG.
"I don't think he will decide on his own. I think he still has a contract in Napoli. It's a big club, and a club that has to be respected like all the other clubs," added Sagnol at a news conference.