Modric, who signed a new six-year-deal last year, was not for sale "at any price," Spurs chairman Daniel Levy said on the club's website.
"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," he added. "They chose to ignore it then 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 the matter closed."
Spurs released the statement after the 25-year-old midfielder, who has not submitted a formal transfer request, told the Daily Mail newspaper he wanted to leave but would like to stay in London.
"Chelsea are a big club with an ambitious owner," he said. "They have great players and they have ambitions to fight for the title and win the Champions League.
"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.
"This is not about money, it is about ambition. When I came to England I was dreaming about winning titles, that is still the same.
"Tottenham are a big club with good players and a good manager but I want to fight for the championship."
Spurs manager Harry Redknapp, who had said on Thursday that Chelsea's initial reported bid of £22 million for the player was "ridiculous," was delighted with his chairman's stance.
Redknapp told talkSPORT radio: "It's a happy thing to have a player like Luka Modric, who has suddenly turned into a £50 million or £40 million player and everyone wants him.
"We're lucky we've got him and we aren't selling him, that's what the chairman says and that's good enough for me.
"The chairman has made a statement today, he can't backtrack on that. He means that, I know he means that. Luka's not going.
"Daniel has made that statement, he can't come out and suddenly sell him. Everyone will go (say) 'What's the use of listening to what he says', he can't sell him, he's said he's not going to sell him and that's good enough for me.
Modric has scored 12 goals in 120 appearances since joining Spurs for £16.5 million in 2008 from Dinamo Zagreb.
