He said he's been following Memphis since 2007-08, Derrick Rose's one and only season at Memphis.
"It's a basketball city," Woodard said. "It's all surrounded by basketball and it's a prestigious school."
It helps matters for Memphis that Woodard has a good friend who's also being recruited by the Tigers in Juwan Parker. The two played together last summer with the Athletes First travel team.
They both took an unofficial visit to Oklahoma last weekend, during which Woodard said Parker raved about his unofficial to Memphis last Wednesday.
"He said nothing but good things, talked about how much he liked it and how hard he was considering to Memphis," Woodard said.
He said he and Parker have discussed the possibility of playing at the next level together.
"If that opportunity seems like it's right, we might pull the trigger on it," Woodard said. "Throughout the summer, we'll stay in touch and it might be a possibility."
Although slightly undersized at 6-foot, Woodard said he's a tough guard with a high basketball IQ. He said his main area for improvement is his overall consistency.
"I can do just about anything on the court fairly well," Woodard said. "I'm working on everything to be great."