Ian Begley of SNY reported Thursday that Rose was "impressed" with Miller's work and "respected the job" he's done since replacing David Fizdale, who was fired in December.
Even if Thibodeau or another high-profile coach is hired to take over the staff, sources told SNY "some prominent people at Madison Square Garden would like to see Miller have a role with the team next season."
The Knicks have posted a 17-27 record since the coaching change.
"If we help these guys and we continue to grow and get better, then we've done our job," Miller told reporters in February. "All I'm concerned about is bringing value to it and helping these guys. As simple as it sounds, I did that for six years as a D-League [and] G-League coach and I felt good at the end of every season. That's the direction that I take."
Miller was named the 2018 NBA G League Coach of the Year.
Along with four seasons leading the Westchester Knicks, he also spent 13 years as a college head coach at Texas State and Eastern Illinois.
Meanwhile, the Knicks were on pace to miss the playoffs for the seventh straight year when the season was postponed indefinitely due to the coronavirus pandemic.