Per ESPN's Ian Begley, a group of people close to Leonard have "expressed a desire" to have him play in New York.
Jabari Young of the San Antonio Express News reported Leonard wants to be traded from the Spurs.
Begley did note there are many teams able to offer the Spurs a better trade package for Leonard than the Knicks, assuming they don't include Kristaps Porzingis.
From the Knicks' perspective, there are two significant issues with Leonard that must be taken into consideration. He can become a free agent after next season by declining his $21.3 million player option, per Spotrac.
There's also the uncertainty about Leonard's health after he missed 73 games last season with a right quad injury.
The Knicks are already entering next season unsure of Porzingis' status as he continues to rehab from a torn ACL suffered in February against the Milwaukee Bucks. General manager Scott Perry told reporters last month they will have a better understanding of where their young star is during training camp in September.
Given the current state of the Knicks, who have missed the playoffs in each of the last five seasons, adding Leonard would certainly make them more interesting than they have been in a long time.