The Italian has only been in the job for a month, but is perhaps taking on the biggest challenge he will likely face in north London in trying to convince the top scoring striker to stay.
Manchester City are keen and reportedly made an 'official proposal', worth at least £100million, for Kane last month.
Having scored 236 goals for Tottenham, it is understood he wants to move to a club capable of winning trophies, but chairman Daniel Levy will not let him go easily, as Paratici explained.
He told Sky in Italy: "Keeping him is not just my goal, it's our goal as a club.
"I can't wait to watch him play live, I've been really lucky in the past years because I've watched a lot of top players and strikers, like Cristiano Ronaldo, Carlos Tevez, Alvaro Morata, Gonzalo Higuain, and many more which now I forgot about.
"Right now, [Kane] is one of the best strikers in the world. He's a complete player, really special. His physique is that of a real number nine, a true poacher, but he also has an incredibly refined technique.
"He is able to shoot with both feet and also provides many assists - very few people notice this, because he scores so many goals.
"He's a team player, but he's a finisher at the same time, so really I believe he is among the top three in the world.
"I haven't heard from him yet because I don't want to bother the players who are busy at the Euros, it doesn't seem fair to me. They're focused on their own goals with their national teams."
Last month, Kane refused to discuss his Tottenham future with his full attention on England's Euro 2020 campaign.
"All my focus is on how I can help this team and how we can be successful in this tournament," he said.
"I understand from a media point of view there is speculation, but I am fully focused on the job here."
However, he has made no secret of his ambition previously as he aims to be considered on a par with Cristiano Ronaldo and Lionel Messi - the two best players in the world.