The 25-year-old has said he wants to leave for Chelsea but will not present a formal transfer request.
Speculation has been rife concerning the Croatia international, with rivals Manchester City and Manchester United reportedly joining the Blues in their pursuit of the player.
It is managerless Chelsea, believed to have already tabled an unsuccessful £22million offer, who appear to offer Modric the most attractive option as he would prefer to remain in the capital.
However, Levy said in a statement posted on the club's official website on Saturday morning: "I wish to make it absolutely clear, as I have said previously, that none of our key players will be sold this summer. We are building a team for the future to consistently play at the highest level and retaining quality players is crucial to that.
"In respect of Luka Modric, we are not prepared to sell, at any price, to Chelsea Football Club or any other club.
"We made our stance on this issue abundantly clear in writing to Chelsea. They chose to ignore it and then subsequently made the offer public.
"For the avoidance of any doubt, let me reiterate that we shall not enter into any negotiations whatsoever, with any club, regarding Luka.
"We now consider this matter closed."
Modric does not wish to enrage Spurs fans but is equally eager to chase for silverware and intends to discuss his future when he returns from holiday, with a switch to Stamford Bridge his preferred outcome.
Tottenham boss Harry Redknapp has repeatedly said his prized midfielder is not for sale and would be unwilling to even entertain offers of less than £30million.
But, speaking to the Daily Mail, Modric said: "If somebody comes to the club and the offer is good for me and acceptable to them, then I want to leave.
"I want to leave Tottenham as friends. I have enjoyed my time there, but now it is right for me to look at another club.
"I have an arrangement with the chairman. When I signed my new contract, he said that, if another club came to sign me, they would consider the offer. I won't ask for a transfer, no. That would be disrespectful. I hope they can reach an agreement that is satisfactory for everyone.
"Chelsea are a big club with an ambitious owner. They have great players and they have ambitions to fight for the title and win the Champions League. I want to stay in London. I am very happy here and so are my family."
Modric said his desire for change was purely a professional one and reiterated his gratitude for Tottenham and their followers.
"I don't want to have an argument with Tottenham. The supporters have been very good to me and I have enjoyed my time playing for the club, but it is for football that players leave clubs and move," he said.
"It has happened to Tottenham before. It is normal for a player to dream about playing for a bigger club."
Spurs full-back Kyle Walker, currently on England Under-21 duty in Denmark, admitted Modric would be a "massive loss" but remained hopeful the north London club would keep hold of him.
Asked how big a gap the former Dinamo Zagreb man would leave for Tottenham if he departed, Walker replied: "He'd be a massive loss.
"But, hopefully, Spurs is not a selling club and hopefully they keep hold of him and keep going forward."
Walker, who has had loan spells with Sheffield United, QPR and Aston Villa since moving to White Hart Lane two years ago, added: "He's a fantastic player, to be fair.
"He's hard to get the ball off in training and he's good to have around, good to give the ball to.
"He gets you out of trouble and I think he's a fantastic player."