There’s one thing Carmelo Anthony and Knicks president Phil Jackson can agree on: The next starting backcourt is more vital than the next head coach.

The need for an upgraded, more athletic backcourt to replace the Jose Calderon-Arron Afflalo pairing is a must for the Knicks to be a playoff team next season.

Anthony has demanded — if not warned — he wants part of the free-agent recruitment process. On Trash-Bag Day Thursday, Anthony acknowledged there are no givens since most clubs possess flowing cap space. Jackson’s first foray into free agency was hardly a splash.

“I don’t want to use the word ‘confident’ because the work still has to be done,” Anthony said. “I think at this point, nobody knows what’s going to happen this offseason with any of the teams, with any free agents. Not until July 1, when the free-agent market picks up. Everybody has that $18-20 million to add to the cap. I don’t think teams really know what’s going to happen.”

Jackson, with his cap space, said he is not obsessing over adding just a point guard for the triangle, which doesn’t require a traditional floor general, but the Knicks need a major boost to take the pressure off Anthony — the kind of boost Afflalo did not always supply.

Given Kevin Durant and LeBron James are pie-in-the-sky, one of the most intriguing names the Knicks have scouted plenty this season is Boston’s 27-year-old free agent Evan Turner, an athletic, 6-foot-7, penetrating swingman who can play the 1, 2 and 3. The sixth man often brings the ball up the court for the Celtics. Jackson and interim coach Kurt Rambis have talked about the franchise needing a penetrator next season.

DeMar DeRozan is the class of the shooting-guard contingent. Who knows what he might do if the Raptors get stunned in the first round by the Pacers? Most predict he remains in Toronto, with his hometown Lakers the top choice if the former USC standout flees.

“I think we have a shot [at a big name], along with everybody else,” Anthony said. “It’s just a matter of a good plan in place — a Plan A, Plan B, Plan C. A lot of things have to fall our way.”

Getting more cap space is a start. A USA Today report Friday stated the cap will go up $2 million more than expected. That would give the Knicks $20 million in cap room, but that’s before dispensing “cap holds” for free agents Lance Thomas and Langston Galloway if they so choose.

The Knicks could gain another $17.7 million in cap room if Afflalo and Derrick Williams, as expected, opt out and Jackson uses a stretch provision on Calderon. Jackson noted their cap space could “double” with certain “machinations” but added Williams and Afflalo gave him no indication of their intentions. Before cap holds, the Knicks could have as much as $37 million in room.

Jackson said he believes there’s more to sell than last summer, when coming off a 17-win campaign with rookie phenom Kristaps Porzingis then a relative unknown except in Latvia and Seville, Spain. The Knicks president also will peddle the 15-game increase in victories that brought them to 32-50.

“We’re talking about a team in the making,” Jackson said. “We’ve had so many people come up to us and say they really want to play for a guy like KP, which is a nice thing to hear from various agents who have players who want to play with a young guy who’s progressing, who has ability to rise in this league, So we feel we have an attractive product here.”

However, the point-guard free-agent class is not star-studded. Even top-of-the-list Mike Conley becomes a risk after being shut down for the season with a major Achilles tendon issue. Anthony already has lobbied for Rajon Rondo, but some in the organization feel he hangs onto the ball too much to be a perfect triangle fit. Brandon Jennings also is free but also not considered as triangle worthy as Ricky Rubio, who likely will be available in a trade.

That is where Jackson and Anthony bump heads. Anthony doesn’t believe brass should rule out certain free agents based on an assumption they wouldn’t mesh in the system that will be employed by either Rambis or a new head coach.

Anthony has a love-hate relationship with the triangle, saying twice in recent days he hates saying the word because of its stigma.

“Guys want to feel comfortable in a system,” Anthony said. “I don’t think guys want to be re-educated about a system or how to play the game of basketball and be in a position they might not be comfortable,” Anthony said. “I think it’s a fine line going after guys who can fit into the system and going after guys who can just play basketball and can bring a winning attitude to this.”

Other shooting guards of note include Bradley Beal, Dwyane Wade, Evan Fournier, ex-Knick Jamal Crawford, Kent Bazemore, Courtney Lee and Allen Crabbe.

Jackson has yet to make the Knicks a destination like they once were.

“I don’t know many guys in the NBA who don’t like coming to New York to play,” Jackson said. “I don’t know how many guys like playing in New York and having to go to that arena as home team. That’s what we got to [change].”