Kentucky coach John Calipari cited two of his forwards as good fits for the big-man-starved Knicks: junior Willie Cauley-Stein to shore up the defense and freshman Trey Lyles to shore up the triangle.

Cauley-Stein worked out for the Knicks on Tuesday, and Lyles was to work out for the club Thursday along with Wisconsin’s Frank Kaminsky.

The Knicks have long been intrigued by Cauley-Stein, a 7-foot defensive specialist who Calipari says could be a future All-Star. Knicks president Phil Jackson has said he would prefer adding a defensive big man over an offense-first one, and could even trade down from the fourth pick for Cauley-Stein.

The 6-foot-10 Lyles is projected to go in the early teens, and the Knicks can also trade down to get him — a definite option if they can obtain extra pieces. Calipari cited Lyles as being a good fit for the triangle because of his outside-shooting ability. Calipari said Jackson shared that assessment when he visited a Kentucky practice in March.

Lyles, who could utilize his 3-point shooting to play as a stretch 4 in the NBA, played at small forward for Calipari because of the plethora of big men on Kentucky’s 38-1 superteam.

“When they came in, Phil (Jackson) watched practice, watched shootaround, watched games,” Calipari said. “What I’m hearing is he walked away saying, ‘This is the kind of player in the triangle who has great (size).’ He’s 6-10.

“We played him at the 3. He could have scored more and done more, but people that really know the game walked away saying, ‘Wait a minute, the kid can shoot, he can pass. He’s really skilled. He’s got size.’ So I think they really liked him.’’

Calipari said he’s heard teams say Lyles is “not assertive’’ because he’s “soft-spoken.”

“The thing they don’t know about Trey, if that fight breaks out, he’s not moving,’’ Calipari said. “He will not move. That’s in him. In a competitive environment, it comes out and you go like, ‘Oh my gosh.’”

A league source said Cauley-Stein had his best workout with the Knicks, but he’s not the post-up guy or polished mid-range shooter the triangle benefits.

“You get a guy that’s 7 foot – he might be bigger – whose feet and hands are that of a 6-3, super athletic guard, which means he can guard five positions, can guard a point guard or a big guy,’’ Calipari said. “He adds shot-blocking. In the schemes of what I’m seeing in the NBA, which are pick and run to the rim and make them play that guy, putting guys in the dribble drive motion, he can do all that. A lot of these kids have been groomed since they were 6 years old. Willie really started playing when he came with us.’’

Cauley-Stein played football and tennis at his Kansas high school in addition to basketball. Calipari noted even Kansas didn’t recruit him.

“He’s not a diamond in the rough, he’ll come in and do things athletically,’’ Calipari said. “You have to mold him offensively and say: ‘This is who you are going to be offensively.’

“I look at Willie for a team that needs defense now to get them to another level,’’ Calipari added. “You take him, mold him offensively and you’ll have an All-Star. His balance needs to improve offensively, getting to the rim and finish and they’ll get to him in one summer.

“I understand the small ball. Small ball is because a 6-7 guy can move his feet and hands like a guard, but now you’ve got a 7-footer that can do the same. He’s unique that he can fly up and down the court.’’

Calipari has heard the rumblings about Cauley-Stein not being “a gym rat’’ who doesn’t love the game because of outside interests. Calipari has spoken to Knicks personnel director Mark Warkentien extensively about Cauley-Stein. Warkentien is close to the Kentucky program because he’s represented by the same agency that reps Calipari — CAA.

“I remember I had three gym rats: Derrick Rose — you couldn’t drag him out of the gym — Brandon Knight and Michael Kidd,’’ Calipari said. “Those guys were in the gym too much. [Willie] loves to play and is coming into his own. Anthony Davis wasn’t a gym rat and he’s OK. He’s well-spoken and fans are going to love him.’’

Knicks announced their summer kids camp dates – July 6-9, 13-16, 20-23 at Baruch; Aug 3-6 at Pace University; Aug 23-25, 26-28 at Ross School in East Hampton.