SNY's Ian Begley reported Thursday that Woodson joins a list of candidates that also includes former Chicago Bulls and Minnesota Timberwolves head coach Tom Thibodeau, former Brooklyn Nets head coach Kenny Atkinson and current Knicks interim head coach Mike Miller.
Woodson, a first-round pick of the Knicks in the 1980 NBA draft, spent 11 seasons as a player with six different organizations before starting his coaching career in 1996.
The 62-year-old Indianapolis native joined New York as an assistant in 2011 and took over as the team's interim head coach during his first season after Mike D'Antoni resigned.
Woodson guided the Knicks to an 18-6 record during the remainder of the 2011-12 season, but they were eliminated by the Miami Heat in the first round of the playoffs. He also led the team to the postseason the following year, advancing to the conference semifinals before being knocked out by the Indiana Pacers.
The Indiana University product posted a 109-79 record across two-plus seasons with the Knicks. The team hasn't reached the playoffs since his departure.
He also spent six years as head coach of the Atlanta Hawks from 2004 through 2010, posting a 206-286 record with postseason berths in each of his final three seasons.
In 2018, Woodson told Marc Berman of the New York Post he craved another chance with the Knicks.
"I don't want to hide the fact I'd love to be back," he said. "I'd like to finish what I started. At the end of the day, you want to come to New York, based on my body of work there. I want it to be mutual. I want them to want me. I hope they call me."
Thibodeau has been viewed as the "strong favorite" to become the Knicks' next head coach based on his relationship with new team president Leon Rose, per Begley.
New York posted a 21-45 record before the 2019-20 NBA season was halted March 11 because of the coronavirus pandemic, and the team isn't part of the league's proposed restart plans.