The Golden State Warriors star is approaching the final few months of his contract, and is expected to become a free agent.
Durant has a player option on an extension for next season, but is not expected to take it.
Instead, the nine-time NBA All-Star is believed to be weighing up his options.
The back-to-back NBA Finals MVP will earn a guaranteed $ 31million (£29 million) if he takes up the option for next year, but will be able to get more if he negotiates from a free agent position.
The Knicks are one of the most likely destinations for Durant next year.
Durant has often been criticised for going to a team that was already good when he joined the Warriors in 2014, and some believe he will want to go to a worse team in order to prove his greatness.
He remained coy when he was asked about the opportunity of joining the Knicks in the summer.
“I have no clue where that stuff comes from,” he said.
“I just focus on playing ball every single day.
“I can’t control what people say about me or what they say about my future or what I should do.
”I just try to come to work every single day and life will figure itself out from here.”
Earlier in the season, Knicks fans funded a banner outside Madison Square Garden depicting Durant in a Knicks jersey holding the Larry O’Brien Championship Trophy.
The mock-up picture was captioned ‘Can you make NY sports great again #KDNY2019’
Durant’s future is one of the most talked-about subjects in basketball right now, as fans wait to see where he will play next year.
Knicks star Kevin Knox even admitted he would love to line up with the small forward.
“It would be cool to learn, work out with him if I play with him and everything he can teach me, a guy that I’ve imaged my game after,” he said.
“To be able to be around him 24/7, that’d be pretty cool, but I’m looking forward to playing against him.”
The Knicks play the Warriors on Tuesday night.
