The latest cycle of hope has arrived for the Celtics. After an uneventful trade deadline last February was followed by a relatively quiet draft night last week, Boston now turns its hopes toward making a big splash in NBA free agency, which begins after midnight Thursday.

The biggest prize of this summer — and there is not even a close second — is All-Star forward Kevin Durant. It remains quite likely that the 2014 NBA MVP will re-sign with the Thunder for one year with a player option for a second season.

But it is also true that Durant does things his own way, so he could make a decision that is unexpected. A league source confirmed that the Celtics are one of the six or seven teams expected to secure a meeting with Durant in New York in the coming days.

For Boston, simply having a seat at the table with one of the game’s elite players could be viewed as a sign of progress. But the Celtics are thinking bigger and hoping this can become more than a courtesy invite.

According to a league source familiar with the Celtics’ approach, the team intends to sell Durant with a simple yet powerful message.

“You tell him the truth, that it’s a good situation,’’ the source said. “Tell him about the ingredients for success that are in place: a good, solid core, the high draft picks to replenish the base, and a great place to play. Arguably one of the best couple of coaches in the league, one of the best general managers, and also a stable ownership group who’s in it to win.’’

The Celtics are the lone team in the Durant sweepstakes currently capable of signing a second free agent to a maximum-salary contract. Of course, most of the others already have one franchise player in place.

Still, Boston’s flexibility and the fact that it holds the Nets’ next two first-round picks — selections that figure to be extremely high once again — should at least make Durant listen. Also, despite the Eastern Conference’s gains and the Cavaliers’ title, the route to the Finals remains less treacherous than it is in the West.

If Durant does sign a one-year deal with the Thunder and this exercise repeats itself next year, this meeting with the Celtics could serve as a kind of dress rehearsal that builds some familiarity to lean on later.

“Maybe this is a warm-up act for next year,’’ a league source said, “and if it is, maybe the deals you do with other players this summer are shorter.’’

Much of how the Celtics approach the rest of the offseason will hinge on their chances of landing Durant. If Durant makes it known that there is a free agent he would like to play with, Boston would certainly do all it can to bring that player in, too.

The Celtics must soon decide how to proceed with forwards Amir Johnson and Jonas Jerebko, whose contracts for next season are not guaranteed. Johnson is slated to make $12 million next season while Jerebko is in line to receive $5 million.

Boston is expected to extend qualifying offers to forwards Jared Sullinger and Tyler Zeller, thus making them restricted free agents and giving the Celtics the right to match any contract offer they receive from another team.

The Celtics have long promised to be aggressive in free agency, and president of basketball operations Danny Ainge said the Celtics’ lack of a draft-day trade was partly due to Boston’s desire to maintain flexibility as it enters this part of the summer.

“We need help,’’ Ainge said. “We need some good players. And we have a lot of really good players. But, yeah, some more good players.’’

The consensus around the league is that most big-name free agents ultimately will stay with their current teams — much like last season. Still, there will be opportunities.

On Wednesday, ESPN reported that the Celtics and Hawks had secured meetings with free agent center Dwight Howard. But a league source told the Globe that Howard is not believed to be “on the radar’’ for the Celtics. The team would be open to sitting down with free agents of Howard’s caliber, the source said, but the price would have to be right to advance in negotiations.

When Howard was linked to Boston in trade talks last February, a league source said the Celtics would be reluctant to offer a long-term deal to a player such as Howard who has had a history of back issues and has questions about his work ethic.

Howard declined his $23.2 million option with the Rockets for next season. He averaged 13.7 points and 11.8 rebounds for Houston last year.

The most logical and attractive target for the Celtics would be Hawks forward Al Horford. It is likely that the former All-Star will re-sign with Atlanta, but he would appear to be a perfect fit for Celtics coach Brad Stevens’s style — a defensive-minded big man capable of stretching the floor with his outside shooting.

Boston was also linked to Horford at the trade deadline in February, but league sources said the team was reluctant to give up assets for a player who would hit the open market just a few months later.

Adam Himmelsbach can be reached at adam.himmelsbach@globe.com..