"Absolutely," Anthony told ESPN's Hannah Storm in an interview for ESPN's "Face2Face." "I'm a big supporter of what coach Woodson has done. His approach to the game, and what he gets out of all his players, even me. He holds everybody accountable and that's what we need."
Woodson took over the Knicks on March 14 when they were six games under .500 and in the midst of a six-game losing streak. Since then, the Knicks have gone 16-6.
The Knicks clinched their second straight playoff berth last week and enter play Tuesday in seventh place in the Eastern Conference, thanks in no small part to Anthony, who is averaging 31 points on 50 percent shooting in April.
The organization also announced Tuesday that interim GM Glen Grunwald will take over as executive vice president and general manager. This may help Woodson's case because Grunwald and Woodson played together at Indiana University and remain close friends.
Anthony has repeatedly credited Woodson for holding players accountable.
He was asked again about supporting Woodson after practice on Tuesday.
The reasons Anthony cited included, "the confidence that [Woodson] instilled into everybody, the belief that he has in everybody. Just his coaching style, the way he's coached, [he's] kind of a hard-nosed coach. [He] holds everybody accountable out there, saying that everybody is responsible for their own actions. I would love to see him back around here."
Amare Stoudemire echoed that sentiment, but not to the same extent as Anthony.
"Coach Woodson has done a great job for us. He's done a phenomenal, phenomenal job," Stoudemire said. "I love his attitude. I love his coaching style. It would be nice [to have him back]."
As he has said in the past, Woodson reiterated on Tuesday that he would "love" to return to the Knicks' bench next season.
"I think when you've been given an opportunity to start something, you'd love to finish it. But again that's not my call," Woodson said. "And I think when that time comes, I'll probably have an opportunity to sit down and talk to [Madison Square Garden chairman] Mr. [James] Dolan and management about it and hopefully it will work in my favor.
"But right now that's not my concern. My concern is finishing these [final] two games [of the regular season] and getting this team in the playoffs. ... That's what it's all about."
Dolan has said that the team would reassess its coaching situation after the season. Many expect the Knicks to go after Phil Jackson, who won two of his 13 championship rings as a player with the Knicks. Jackson is currently retired from basketball. Kentucky coach John Calipari could also be a candidate. He has denied interest in leaving Kentucky.
If Woodson isn't retained by the Knicks, there should be several suitors for his services. But, according to two sources with knowledge of Woodson's thinking, his priority is to return to New York.
The former Hawks head coach took over for Mike D'Antoni on March 14 after D'Antoni and the organization mutually agreed to part ways.
There was rampant speculation that one of the main reasons for the coaching change was a rift between D'Antoni and Anthony.
In the interview with Storm, Anthony said he never had a problem with D'Antoni.
Anthony did raise eyebrows shortly after Woodson took over when he said he and his teammates were playing with an energy level and commitment to defense that wasn't there under D'Antoni.
"Me and Coach Mike never had any arguments, we never had any clashes or any disagreements," Anthony said. "We communicated. If it was something that he didn't like, I always went to him and said, 'Coach, come to me, let me know what you don't like; if it's something I'm doing, if it's something I'm not doing. As long as me and you is on the same page, none of this outside stuff should be [affecting us].' "
"I think it just became a lot of pressure from his standpoint, from my standpoint and then losing basketball games at the same time," Anthony added. "And who else were they going to put [as] the Clash of the Titans? It was me and Coach Mike."
Ian Begley is a regular contributor to ESPNNewYork.com.