Can USC keep Mayo for second season?

If it’s fun, then O.J. Mayo might not be one and done.

The most coveted recruit in USC basketball history said Friday afternoon that if the Trojans fall short of a national title in his freshman season but show promise for the following year, he might not necessarily bolt for the NBA.

“I just want to win, so if we come really, really close next year and are a player or two away and go out that [spring] and grab the pieces that we’re missing, then of course I’ll come back,” Mayo said shortly after arriving on campus for his official visit. “I want to win at every level.”

While acknowledging that the opportunity to play for a former NBA coach and promote himself in one of nation’s largest media markets were attractive lures, Mayo said his primary enticement was winning.

The 6-foot-5 point guard from Huntington (W.Va.) High said he felt the Trojans provided “the best chance to win a national title” considering the players Coach Tim Floyd had recruited for next season. Mayo is the biggest catch in a recruiting class ranked No. 2 nationally by rivals.com.

Another attraction was the Southern California climate. Noting that it was 30 degrees Friday in his hometown, Mayo said he loved the idea of living in Los Angeles.

“I like the city of L.A. It’s a great city,” he said. “I just think it needs the opportunity for a great basketball team to represent it. I know UCLA’s been doing their thing for a long time. It’s a new time.”

Already projected by some as the No. 1 overall pick in whichever NBA draft he decides to enter, Mayo averaged 28.6 points, 5.7 rebounds, 5.0 assists and 2.3 steals last season for Cincinnati North College Hill High, which won a second consecutive Ohio state Division III title. Mayo said when he first broached the idea of playing basketball in Southern California with Rodney Guillory, an advisor to Mayo who lives in Los Angeles, Guillory suggested UCLA.

“I was like, ‘Nah, USC,’ ” Mayo said. “UCLA has won championships and has a great history. History has to start from somewhere, and I was thinking maybe getting USC turned around.”

Mayo arrived at Heritage Hall early Friday afternoon to great fanfare, with a documentary camera crew and entourage in tow. He hugged Athletic Director Mike Garrett and was besieged for autographs by children who instantly recognized him. Mayo said he recently told his hometown newspaper that he would visit five schools and wait until the spring before making a decision because he was trying to placate his family, which “wanted me to see some other universities before I put all my eggs in one basket.”

But Mayo went ahead and signed with USC on Wednesday, he said, because he “didn’t want to waste anyone’s time. I knew I didn’t have any interest anywhere else, so I just wanted to get it over before the [high school] season.”

Mayo said his mother, initially reluctant for him to attend a school so far from home, was now on board with his decision because she realized how much he wanted to come to USC.

Floyd, who had publicly acknowledged that he expected Mayo to be on campus for only one season, said Friday that “it’s far too early to even speculate on those things. The most important thing is him getting himself established here at the university and try to have as good a year as he could possibly have. All those things will be weighed out in the future, and that will be O.J. and his family’s decision. If they ask for my advice, I’ll give them my advice.”

Other schools that interested Mayo included Florida, Connecticut and Kansas State, he said. Mayo said the first two schools fell off his list after he visited USC over the summer. Kansas State is no longer an option because Mayo’s close friend and former high school teammate Bill Walker became a Wildcat this season and is likely to declare for the NBA draft before Mayo could join him.

Mayo said he had researched USC’s incoming recruits and waited until highly touted forward Davon Jefferson signed a letter of intent before following suit. Mayo said he believed the current Trojans roster, combined with the incoming recruits, was sufficient for a run at a national title.

“I think it’s time for this program to turn it around,” Mayo said. “They win national championships in everything except basketball, so I’d like to be the first one to be a part of that.”

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ben.bolch@latimes.com