Tottenham chairman Daniel Levy is reportedly considering whether to report the club to the Premier League for continuing to pursue the 25-year-old Croatian.
Modric has five years remaining on his six-year, £45,000-a-week contract with Spurs but a move to Stamford Bridge would likely triple his salary to £130,000 a week.
In a statement today, Levy said: "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 or any other club. We made our stance on this issue abundantly clear in writing to Chelsea. They chose to ignore it and 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."
Spurs manager Harry Redknapp said that it would be "difficult" for the club to keep hold of Modric if he wants to leave. "He's ambitious and he's probably got a chance to treble his wages," he said.
"But if we sell Luka Modric, where are we going as a football club? We have to accept we are then a middle-of-the-table team that will finish hopefully in the top half next season."
He added: "The chairman has made a statement and he can't backtrack on that. He can't come and suddenly sell him because everyone will go, 'What's the worth of listening to him?'"