The Knicks are 2-8 to begin the 2019-20 campaign, and Isola reported "time may be running out" for current Knicks president Steve Mills.
Ujiri is one of the most proven executives in the NBA. He won Executive of the Year with the Denver Nuggets in 2012-13 before transforming the Raptors into a contender and eventually a champion last season.
New York eventually settled on Mills as president and Scott Perry as its general manager.
"For me it's always been about Toronto," he said in June, per TSN. "I love it here. My family loves it here. My wife loves it here, which is important. My kids are Canadian. I want to win more. ... In my mind, I'm here."
That could make it difficult for the Knicks to change his mind. However, Isola noted Ujiri could "put the Knicks in play for Giannis Antetokounmpo."
After failing to land any of the biggest names on the free-agent market this past offseason, Dolan might do whatever it takes to get an executive who can produce better results going forward.