Bobby Marks breaks down key desires for the Spurs and the Celtics in potential Kawhi Leonard deals and what would prevent Boston from doing a deal. (1:27)

BOSTON -- Boston Celtics president of basketball operations Danny Ainge said it's his job to explore all trade possibilities when superstars become available but gushed about his current core and deemed the possibility of his team completing another summer blockbuster trade as unlikely.

The Celtics, armed with their treasure trove of young talent and future draft picks, have the necessary assets to put together maybe the best possible package for a player like San Antonio's Kawhi Leonard. And while Ainge stressed that he couldn't talk specifically about any free agents or players in trade rumors, he made clear Friday that it's simply his job to explore all possibilities involving elite-level talent.

"If I feel like it'll help our team -- we explore every trade of players of certain magnitude or superstar, first-ballot Hall of Fame-type of players," Ainge said Friday after the Celtics formally introduced first-round pick Robert Williams at the Auerbach Center. "We're going to take a look and kick the tires and see if there's something there. But that's all.

"I think those things are unlikely."

Ainge admitted that the Celtics are in a quality position with the ability to thrust themselves into any pursuit of star talent -- like they did a year ago when they acquired Kyrie Irving from the Cleveland Cavaliers -- but he also gushed about the potential of his current roster.

"I feel great that we have a lot of players that people like and want," Ainge said. "That's a great feeling to have. That's not always the case, and that's the reason we like our guys, too, is we have a lot of talent on our team. I'm excited about our team going forward."

Ainge believes Boston is a title contender as currently constituted. The Celtics took the Cavaliers to Game 7 of the Eastern Conference finals before bowing despite playing without stars Irving and Gordon Hayward.

"Yes," Ainge said when asked if Boston is a title contender with this roster. "I felt like we were a title contender last year in training camp. I didn't think we were the favorites, but I felt like we were a contender."

Asked about how Boston's collection of desirable assets invariably leads to the Celtics being lumped into a bevy of trade rumors, regardless of how serious Boston's interest is, Ainge did lament having to mend fences with players whose feelings are hurt by the suggestion they might be moved.

"I think that most of [the rumors are] false. Especially the details of it," Ainge said. "And what I don't like about it is, I don't like how names are just thrown around [in media reports]. [Reporters] probably don't care about the names, and that's your job is to make good stories and have things to talk about on the air. Most of it's not true, but there's sometimes bits and pieces of it that are true. So it's not total lies, but -- I can't call it fake news -- but it's complex.

"These are complex situations, and I think that, just like [reporters] don't like answering or having to respond to rumors, even though it does give you good programming, I don't like it any more, having to deal with the players that are calling me and the agents that are calling me when their name is in a rumor that's, like, just totally made up."

The Celtics tendered a $6.1 million qualifying offer to Marcus Smart on Thursday, making him a restricted free agent. Both Smart and unrestricted free agent Aron Baynes are two players Ainge has suggested the team wants back, and the Celtics will work to keep them as part of their core.

Ainge said the team is looking at all possible upgrades this summer but doesn't feel a need to find a specific type of player.

"It's easier when you have three [star] guys already that you've gotten from the years before and you got some budding stars in younger players that are progressing. So ... we don't really have a need. We have really good players.

"And so we need to surround them with role players with the rest of our roster that have a chance to win."

Williams will wear No. 44, Ainge's old jersey number, and Ainge went out of his way to squash concerns about the rookie's work ethic and motor, which contributed to him sliding out of the lottery and to Boston at No. 27 in last week's draft.

"It's hard to have a low motor and be defensive player of the year for two years in a row in a tough conference," Ainge said of Williams. "I've heard the same types of criticism, but that's a hard thing to do."