ESPN.com reported Thursday the Knicks have yet to contact Griffin but added they have been gathering background information and contacted someone in the Cavs front office to ask about him.
The Knicks announced Wednesday they agreed to mutually part ways with Jackson.
ESPN.com also reported Thursday that Griffin has long coveted high-profile jobs. Attempting to lead the Knicks back to glory would undoubtedly qualify.
Adrian Wojnarowski of The Vertical reported Wednesday the Knicks were considering Toronto Raptors GM Masai Ujiri as Jackson's replacement.
Landing Ujiri could prove difficult, however, since the Knicks would likely have to part with draft-pick compensation due to his being under contract.
Griffin and the Cavaliers parted ways shortly after Cleveland lost in five games to the Golden State Warriors in the 2017 NBA Finals.
After being named Cavs general manager in 2014, Griffin was among the architects who built the team and helped lead it to three consecutive NBA Finals and one championship.
The Knicks haven't reached the playoffs since 2012-13, and they lost at least 50 games in each of their three full seasons under Jackson.
Should Griffin be tabbed for the job, he will have some young pieces to build around in big man Kristaps Porzingis and 2017 first-round draft pick Frank Ntilikina.