Knicks president Phil Jackson would like Andrea Bargnani back for the right price because of his skill set for the triangle offense.

And in an interview with an Italian sports newspaper, Bargnani indicated he would like to return to the Knicks — but winning a championship is also a factor in his decision. The Knicks had the league’s second-worst record in 2014-15 at 17-65.

Bargnani played in 29 games after not making his season debut until New Year’s Eve because of a series of hamstring and calf injuries. However, Bargnani may have showed enough to merit a free-agent offer in excess of the veteran’s minimum of $1.4 million, according to two league executives. The league executives do not believe he will get more than a one-year deal, however.

Jackson probably won’t dip into his cap space to re-sign the enigmatic 7-foot Italian, who posted four 25-point games down the stretch, including one outing in which he blocked four shots. However, Jackson can sign exceed the cap to re-sign his own player, such as Bargnani. But even if Jackson makes a competitive offer, Bargnani is no lock to re-sign.

“I had a great experience with the Knicks, I liked the city, the team and had a good relationship with Derek Fisher,’’ Bargnani told La Gazzetta DelloSport in his native tongue. “I wouldn’t mind signing with the Knicks if the opportunity comes. I will let my agent do his job starting July 1. I am now a veteran in the NBA, and, you know, I would like to sign with a team that can give me the opportunity to win a ring.”

The translation was provided by the author, New York-based Italian writer, Simone Sandri, who spoke to Bargnani by phone and attends many Knicks contests. The Knicks did not make Bargnani available to the press after the season finale. Bargnani was not with the club for the final four games as he battled a respiratory illness.

It had been assumed if Bargnani, who will play next season at age 30, didn’t have any bigger offers, he would come back to the Knicks for the veteran’s minimum. But evidently other factors are at work. His free-agent market value will be one of the big mysteries of summer. He hasn’t played more than 42 games in any of the past four seasons.

“We certainly didn’t live up to expectations,” Bargnani told the Italian paper. “The beginning of the season we all thought we’d get to the playoffs, then things went differently and, injuries aside, I can not give a real explanation . For me it was very frustrating not being able to lend a hand to my teammates in the first half of the season. When I came back, I think I did well, so I’m pretty satisfied. In the end of the season, we also found a little confidence with the triangle.’’

Bargnani played best working in pick-and-roll situations with Russian combo guard Alexey Shved, whose return to the Knicks is also considered questionable. Bargnani finished the season averaging 14.9 points and 4.4 rebounds, shooting 45.4 percent.

He told the newspaper he likely will play for the Italian National Team in this summer’s Euro Cup.