But Knicks star Carmelo Anthony believes the coach is safe.
"As far as I'm concerned, he's secure right now. I haven't heard anything," Anthony said Monday night after initially declining to answer a question about Woodson's potential status. "There's nothing to discuss. He's our coach, and we're rolling with him."
Woodson's job security has come into question in recent weeks with the Knicks (7-17) playing well below expectations. Two crucial late-game errors Monday only put more heat on the coach.
New York had a one-point lead with 24 seconds to play and a foul to give. Instead of using the foul, the Knicks allowed Bradley Beal to drive for an uncontested layup with 6.9 seconds left.
Then no one called for a timeout, and no final play was set up. Instead, Anthony dribbled the ball across half court and took an off-balance, 25-foot shot that fell short as time expired.
The Knicks had three timeouts remaining.
"I probably should have taken a timeout there at the end," Woodson said, "but you know, Beno [Udrih] grabbed it [to inbound] and the ball is in Melo's hands before I could even react, and I should have reacted a lot sooner once the ball went through the bucket.
"So that's on me. I didn't call the timeout, so I've got to take the heat for that."
The coach said he instructed his players to give a foul on the Wizards' final possession. Instead, Udrih gave Beal the baseline.
Woodson said Udrih expected Andrea Bargnani to help stop Beal from getting to the rim. That help never came. Beal converted an uncontested layup, sending the Knicks to their ninth home loss in 13 games.
"That's a tough way to lose a game," Anthony said after scoring 32 points. "If [Woodson] said it's his fault, there's no need for me to make excuses or talk about it. As players, we have to be smarter. We knew we had timeouts. I was just trying to get a shot."
The Knicks had lost 11 of 13 prior to a win Wednesday over Chicago, so there has been speculation throughout the month that Woodson's job is in danger.
Team owner James Dolan gave Woodson a public vote of confidence Nov. 20. But the Knicks have gone 4-9 since Dolan's comments, including a 41-point loss to Boston on Dec. 8 and a 15-point loss to Cleveland two days later.
A source with knowledge of the team's thinking told ESPNNewYork.com last week that Woodson is being evaluated on a "game-by-game basis" by upper management.
Woodson is under contract through next season, but his salary likely wouldn't impede Dolan if he wanted to make a change.