We are about to find out about the NBA’s new normal.

Know this for sure: It will include contracts with many, many zeros as teams line up to throw bags of newly minted money at players.

Free agency begins at 11:01 p.m. Thursday, kicking off a week of negotiations. Starting July 7 teams can officially announce just how much money they spent and on whom.

It will be a lot. The league’s new $24 billion TV contract is set to kick in, and that will have an enormous impact on the salary cap, which is going from $70 million to as much as $94 million, or perhaps even a little more.

That means a lot of teams will have a lot of money to spend. The Timberwolves, for example, will have more than $25 million in cap space, should they decide to spend all of it.

A lot of other teams will have much more, and just about every team will have enough to make a splash.

With that in mind, Wolves President of Basketball Operations and coach Tom Thibodeau was asked if he had a good feel for what the NBA’s new normal would be after first-round draft pick Kris Dunn was introduced last week.

“I don’t,” he said. “But it’s exciting. As you prepare, you sort of try to figure out the tiers. Where people may fall. But you don’t know how it unfolds until it actually starts.”

It could get crazy.

Leave out for a moment the top tier of free agents. Oklahoma City forward Kevin Durant and his agent have reportedly set up meetings with five other clubs with reps traveling to the Hamptons to meet with him, ready to give him a max contract in the area of $27-plus million per year. Already he’s being recruited by the likes of fellow Olympian Carmelo Anthony, who is trying to woo him to the New York Knicks. LeBron James has opted out of his contract. He’ll likely stay in Cleveland, but get paid more; he might take a one-year deal so he can take advantage of a cap figure that will again jump significantly in 2017.

Where the real impact of the cap will be seen is in how much very, very good players might get.

Already there is talk of players like Memphis guard Mike Conley, Atlanta’s Al Horford and Charlotte’s Nicolas Batum getting at or close to max money, though some will stay with their teams. Miami center Hassan Whiteside is also looking for max money.

It’s no secret Dwight Howard wanted out of Houston anyway. But he opted out of $23.2 million to do it. Other players who have walked away from guaranteed money to test the market include Chicago’s Pau Gasol (who was due $7.769 million), Toronto’s Bismack Biyombo ($2.8 million) and Cleveland’s J.R. Smith ($5.3 million).

Look for big raises. Indeed, Toronto star DeMar DeRozan opted out of his contract of $10.2 million and could get a five-year, $153 million dollar deal to stay with the Raptors.

Even Chicago’s Joakim Noah, whose numbers have declined steadily the last two years, and who had season-ending shoulder surgery 29 games into last season, has attracted big-money interest.

Noah, who averaged just 4.3 points and 8.8 rebounds last season, is getting interest from New York (where former Bull Derrick Rose is recruiting him) and Brooklyn.

The Wolves, too, are assumed to be in the hunt for Noah, who used to play for Thibodeau.

“You can tier it out, in terms of who the player is,” Thibodeau said. “Is it a starter or a backup? Is it a young guy, an older guy and what is his situation? You try to prepare yourself that way. Then you look at your own team and what your needs are.”

Thibodeau’s list of needs sounds familiar: “You can never have enough shooting,” he said. “Size, toughness, shooting. Those are things we’re looking for.”

One thing you likely won’t hear about is Thibodeau and GM Scott Layden jumping plane for a midnight presentation. “We’ll do our homework and have everything prioritized,” Thibodeau said. “And I think most players aren’t responding to that stuff. So our experience just tells us to be prepared. We feel what we have to offer is our team, and we want serious-minded players committed to winning. We feel we have a lot to offer.’’