CLEVELAND -- Derrick Williams, signed by the Cavaliers to a 10-day contract this week, will be sticking around Cleveland for a while -- if LeBron James has his say, at least.

"We hope that this is a long-term thing," James said of Williams after the Cavs' 125-109 win over the Denver Nuggets on Saturday. "Obviously, we know that he's on a 10-day contract, but we believe it's going to be long-term."

Williams had seven points in 21 minutes against the Nuggets and played the entire second quarter when Cleveland outscored Denver 31-22.

The Cavaliers are the fifth team the six-year veteran has played for since he was selected with the No. 2 pick in the 2011 draft.

"He's been in some difficult situations, first of all, and we hope that this is a place that can help him grow and make that next step," James continued. "He's 25 years old. It doesn't seem like it because we've been hearing his name for so long. But he's 25. He hasn't even gotten to his potential, to his prime yet, so hopefully this group, this locker room, myself, my leadership [helps him]. Just want to see him grow every day, and it's a good place for him."

For Williams, who is averaging 9.5 points on 83.3 percent shooting in his first two games with the Cavs, playing in front of a sell-out crowd at Quicken Loans Arena was a revelation.

"Atmosphere was great, man," Williams said. "I hadn't experienced anything like that since I've been in the NBA. Just taking it all in. Just trying to help this team win. That's what I'm here for. Just play with energy, play with effort, play with efficiency and try to get a win. That's why I'm here."

Derrick Williams was waived by the Heat on Monday to sign a 10-day contract with Cleveland. Jason Miller/Getty Images

Williams has shown some versatility thus far, guarding opposing point guards and even taking the ball up to get the Cavs into their offense. He was part of a plus-sized Cleveland lineup with James, Kyle Korver, Channing Frye and Richard Jefferson in the second quarter -- all measured 6-foot-7 or taller.

"I did like it because defensively we could switch 1-through-4 with those guys and kind of stay at home, and then we could run the floor and could play with big pace," Cavs coach Tyronn Lue said. "And also what helps us with that is now they got to put a point guard on Korver when they can't switch out onto all our stuff with our second unit, so that's why I like it and want to take a look at it."

Although Williams is still waiting on a long-term commitment from the team, he did make himself more at home by changing to a preferred uniform number. He wore No. 32 against Oklahoma City but had No. 3 on against Denver. "I've worn pretty much a different number on every team I've been on, so I'm trying to switch it up a little bit and see which one's a little more lucky," Williams told ESPN. "My mom was like, 'You played so well in No. 32. I don't know if you should switch it.' I was like, 'eh, I'll be all right.' I'm not superstitious or nothing."

But he is realistic. While it appears he has already acquitted himself well, there was sizable risk involved to coming to Cleveland on a non-guaranteed deal with a team that has been open about its search for an additional point guard or rim protector.

"I kind of put myself in this predicament," Williams said. "I asked for the release from the last team, and I put myself in a 10-day. So I'm not worried about anything after that. I just want to take every day at a time and put myself in a position I've never been in, and that's what I want to do, and that's why I chose to come here."

Based on the way James has rolled out the welcome mat already, Williams shouldn't have much to worry about.

"We're happy to have him," James said. "It's not many places you're going to find a 6-[foot]-8 wing with athleticism like that at 25. So we're lucky to have him."