SALT LAKE CITY -- Gordon Hayward improved his scoring average in each of his first six NBA seasons, earned a maximum contract and is virtually guaranteed to get a large raise this season, assuming he decides to opt out of the final season of his deal with the Utah Jazz.

Hayward, however, hasn't been good enough. Just ask him.

"I'm definitely not satisfied with what I've done so far in my NBA career, and I think that I've got to be a better player for us to be where I want us to be," Hayward told ESPN. "For us to be in the playoffs, to make a splash, to compete at a higher level, I have to be a better player."

Hayward has put up some pretty impressive individual numbers. For instance, he's one of five players to record at least 4,000 points, 1,000 rebounds, 1,000 assists and 350 made 3-pointers over the previous three seasons, along with Stephen Curry, LeBron James, James Harden and Kyle Lowry.

Hayward is the only player on that short list who hasn't been an All-Star. The Jazz believe that could and should change this season, with Hayward hitting the ground running after missing the first six games with a broken left ring finger. As Utah's go-to guy, he is averaging 22.5 points, 7.0 rebounds and 4.0 assists in his first six games.

"I look at him and think we've got a player that's on that level," Utah coach Quin Snyder said. "No question in my mind."

There is also no question in Snyder's mind that Hayward, 26, is capable of being a franchise player for a team that not only makes the playoffs but can do some damage once it gets there. That's what matters to Hayward. That's what motivated him when he arrived at the team facility by 7 a.m. at the latest for daily workouts with assistant coach Johnnie Bryant every day this summer, the first full offseason he spent in Salt Lake City.

When the Jazz drafted Hayward with the ninth overall pick in 2010, he joined a perennial playoff team led by legendary head coach Jerry Sloan and All-Star point guard Deron Williams. They were both gone before Hayward's rookie season ended. His only taste of the playoffs so far came in his second season, when the Jazz were swept in the first round by the San Antonio Spurs.

Utah has been in rebuilding mode since. As far as Hayward is concerned, that's in the past tense.

"We're out of that phase, and we're trying to win basketball games," Hayward said. "We definitely have a good thing going for us."

The future certainly seems bright for the Jazz, who are off to a 7-5 start even though their starting lineup played only one game together. Hayward, power forward Derrick Favors and point guard George Hill have all missed extended time because of injuries.

Hayward, Favors, center Rudy Gobert and shooting guard Rodney Hood make up an intriguing core of 26-and-under talent with enough experience to be expected to end Utah's playoff drought. Jazz general manager Dennis Lindsey made savvy offseason moves to add three accomplished veterans in Hill, Joe Johnson and Boris Diaw. Hill, in particular, has been a terrific addition and has the potential to be a long-term fit.

But the Jazz will only be as good as Hayward. That's a responsibility he embraces, which is why he refuses to settle for being a very good player.

"He proved, in my mind, to be more hungry than maybe you thought at first glance," Snyder said. "When you're a very, very good NBA player, sometimes that's enough. In his case, 'No, I want to be a great player.' It's one thing to say that. It's another thing to put in the time in order to do that."

Under Bryant's supervision, Hayward focused this summer on two specific facets of his game: balance and footwork. The Jazz coaching staff believed Hayward often worked too hard for his buckets, overdribbling at times because he wasn't technically sound enough. Hayward accepted the challenge, mixing in some boxing to improve his footwork, along with his weight lifting and basketball drills.

"His approach of really dialing in and really targeting his game in terms of fine-tuning certain areas, that's where he's made the biggest leap and jump in my opinion over the years," Bryant said.

Bryant believes Hayward has made a significant leap the past two seasons in large part because he became a family man, forcing him to narrow his focus. Hayward agrees, saying his marriage to wife Robyn and the arrival of young daughters Bernadette and Charlotte, who was born July 11, made him prioritize things in his life and become more professional.

Robyn being pregnant with "Charlie" was one of the primary reasons Hayward opted to stay in Salt Lake City over the summer. He turned down an invitation to play for Team USA and didn't want to move a pregnant wife and toddler daughter across the country.

The Jazz hope they've given Hayward plenty of reasons to stay in Salt Lake City for the long term. They plan for him to be the centerpiece of a franchise that snaps a five-year playoff drought with a multiyear run of postseason appearances.

"Gordon's a smart guy," Snyder said. "He's going to know what he needs and what he wants. My personal feeling is, he's got everything he needs right here. I think there's a fit. There's a lot of positives, and there's a lot of things that fit. In the end, he's got to feel good about that."

Hayward is happy, if not satisfied, in Utah. He's not ready to commit to re-signing with the Jazz, but that's partially because he doesn't want to clutter his mind with business when the Jazz finally seem primed to make the playoffs again.

"For me, I realized from that first year that anything can happen and anything can change," Hayward said. "Really, as a basketball player in this business, when you start to worry about where you're going to be in the future and what's going to happen the next couple of years, that's when you start to get distracted and you start to not play as well and things start to slip away. I've always been told to control what I can control. For me this year, that's helping the Jazz win as many basketball games as I can, and that's honestly what my focus is on.

"As far as what's going to happen in the future, I don't have a magic lamp or anything to say what the future holds. For me, I'm here right now and happy to be in Salt Lake, happy to play for the Jazz and excited for our upcoming season."