Per Marc Stein of the New York Times, Rich Kleiman is making a behind-the-scenes push for the Knicks to hire Jackson.
Stein added that Kleiman has been a lifelong fan of the Knicks and has personal relationships with Jackson and Knicks president Steve Mills.
Jackson was one of the candidates interviewed by the Knicks for their vacant head-coaching job. Jeff Hornacek was fired last month after going 60-104 in two seasons with the team.
ESPN's Adrian Wojnarowski reported Tuesday that the Knicks finished their interviews with the hope of hiring a new coach this week.
Stein noted David Blatt, Mike Budenholzer and David Fizdale are regarded as the prime contenders to be hired by New York.
Jackson played seven seasons for the Knicks during his playing career. He spent three seasons as head coach of the Golden State Warriors from 2011-14, compiling a 121-109 record with two playoff appearances.