DENVER — Chauncey Billups, twice a teammate of Carmelo Anthony’s, says the Knicks star needs an elite point guard this summer to flourish and is skeptical the club will find one if the organization sticks religiously to Phil Jackson’s triangle offense.

In candid comments five years after he and Anthony were traded together from Denver to the Knicks in a trade-deadline blockbuster, Billups told The Post his former compadre has maybe four years left in his prime, but time is starting to tick away and he feels Melo’s pain.

Anthony returns to Denver for a game Tuesday against the Nuggets and the struggling club will practice in the Mile High City Monday to get acclimated to the altitude.

Billups, the former All-Star point guard who won a title with Detroit, still lives in his native Denver, commuting to work as an ESPN studio analyst.

“I would be growing impatient if my prime years were slipping away,’’ Billups told The Post Sunday in a phone interview regarding the 31-year-old Anthony. “But this is what he chose — not once, but twice.’’

Billups, amnestied by the Knicks after the 2010-11 season to open cap space to sign Tyson Chandler, is glad to hear Jackson’s recent missive about being flexible with the triangle.

“I will tell you this about that triangle,’’ Billups said. “If I’m a top point guard and a free agent, I’m not going to want to be playing in that triangle. A point guard needs more pick-and-roll, more freedom. It’s going to be restrictive to my play. I think that would be a good thing — if they are opening it up a little. It’s the only way to get a point guard.’’

Billups ignited Anthony to his best season in 2008-09, when the Nuggets advanced to the Western Conference Finals and lost a taut six-game series to the Lakers. Billups laments that series loss, feeling it came down to two late-game botched possessions off inbounds plays. He still feels the Nuggets could’ve done major damage if Anthony and Billups stayed in Denver and Anthony didn’t demand a trade. Now Anthony is on the verge of missing the playoffs a third straight season.

“I think Melo’s still in his prime, I do,’’ Billups said. “Melo still will be in his prime another four years or so. I still think he’s a matchup problem — one of the most unstoppable guys in the league. One thing about Melo, he needs to have good players around him. They made some upgrades to the roster but not enough. You got to have a really strong point guard with him that knows how to get him the ball, when to get him the ball and when not to get it to him. He’s at his best playing like that.’’

The Knicks’ point guards are Jose Calderon, Langston Galloway and rookie Jerian Grant.

“More than any other time in the league, it’s important to have an elite point guard,’’ Billups said. “It’s a guard’s league. Most top point guards are lead guards who can get it done. No disrespect to anyone in a Knicks jersey, they don’t have a guy on the roster who plays that position who can do that.’’

Billups said he was disappointed to be dealt from his hometown team, feeling the Nuggets were on the cusp of more special things before getting derailed when coach George Karl fell ill.

“[Anthony] made one helluva move five years ago,’’ Billups said. “We were inching and inching closer to winning it. We were two plays away from [beating L.A.] and winning the West and we could’ve easily beaten Orlando. That’s how close we were to winning it in Denver. So [Anthony] has tasted it a bit. Now you go to a place where he always wanted to play and can’t even make the playoffs. That’s tough.

“It’s something Melo wanted to happen, going to New York, which was understandable, him going home, being born in New York, East Coast guy. He was very, very excited. Me on the other hand, I [wasn’t].”

Billups still confers with Anthony and gave him advice when he became a free agent in 2014.

“I honestly felt the best chance to win would’ve been to go to Chicago,” Billups said. “It would’ve been great — a tough-minded coach in [Tom] Thibodeau at the time and other players around him where he didn’t have to be great every single night. Obviously it was a sacrifice. A lot of money he had to leave on the table, but you sign three years, win and he would’ve gotten more money anyway.”