"There has been nothing. No discussions. No plans to have discussions -- nothing," the company said in a statement.
In a The Ringer podcast, host Bill Simmons said Dolan was "courting offers for the Knicks."
The Madison Square Garden Company said in a statement that "the story is 100 percent false."
Dolan said in an interview with ESPN's Ian O'Connor late last year that he couldn't rule out selling the Knicks if the right offer came along.
Dolan said in the interview, which was published in December, that there have been "feelers" of offers upward of $5 billion for the Knicks, but that "no one has come through with a bona fide offer."
"You hear numbers all the time," Dolan said. "... I think people have sent feelers out, but never any that were pursued. Yeah, [the feelers are] around that number [$5 billion], but those things, it's like a stock price. It's only important if you're going to buy or sell."
Dolan said in the interview that he loves the Knicks and Rangers, "but you still have a responsibility to your shareholders."
"You have a responsibility as the guy who runs the place to deliver on that for them -- that's being open and transparent. And so in that position, I could never say that I wouldn't consider selling the Knicks. Now, my family is not in that position, and they are the majority shareholders. They hold the majority of the vote. ... As a majority owner, I don't want to sell, either. As the head of the public company, you can't say you can't sell, because then you're telling your shareholders that your own personal feelings about your assets are more important than their money. And they won't invest with you if you do that."
Dolan took over as chairman of Madison Square Garden in 1999. The Knicks made the NBA Finals in his first year. They haven't been back since, as the team has gone through seven team presidents and 12 head coaches. They have won just one playoff series since 2000-01 and currently have the second-worst record in the NBA.
The losing hasn't impacted the overall valuation of the franchise, according to one measurement. Earlier this month, Forbes ranked the Knicks as the NBA's most valuable franchise, worth $4 billion.
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