• The world number 45's run to his first Grand Slam final saw him fined for several outbursts on court.
• McEnroe says he asked Kyrgios on "numerous occasions to come and have a chit chat" but he always find "an excuse".
John McEnroe says Wimbledon runner-up Nick Kyrgios has "got his demons" but tennis needs him "big time".
Australia's Kyrgios, 27, was beaten by Serbia's top seed Novak Djokovic in Sunday's men's final.
The world number 45's run to his first Grand Slam final saw him fined for several outbursts on court.
McEnroe says he asked Kyrgios on "numerous occasions to come and have a chit chat" but he always find "an excuse".
"I get a lot of what's going on here more than most people," the American, 63, told BBC Radio 5 Live Breakfast.
"He's a good kid, the players like him, he's well liked in the locker room, he does a lot of charity work.
"But he's got demons you know, in a way - we all have this fear of failure and it's a question of how you best deal with it."
Kyrgios' run to the final came amid more controversy as it was revealed he faces a court hearing in Canberra next month in relation to an allegation of common assault.
Seven-time Grand Slam champion McEnroe said the shots Kyrgios pulls off are "incredible", adding: "It's unbelievable so he moves the needle for us in tennis. We need this big time, but we don't need him to try half the time.
"Who should coach Nick Kyrgios? John McEnroe of course but he's untouchable. Anyway the guy doesn't need the coach, the guy is a genius out there the way he plays. He needs Sigmund Freud to come out of the grave and somehow figure out a way to keep this guy going for a couple of years because we could use him."
Speaking to BBC Sport's Laura Scott, McEnroe added: "You know he's sitting there and he's obviously tortured in certain ways. [He's] unbelievably talented, very smart.
"[He's] a hell of a player when he wants to be and so you want to nurture that in a way as an ex-player, as a father, as a fan, as a commentator, so I can relate a lot."
'There's certain behaviour I regret'
McEnroe explores mental health, among other topics, in an upcoming documentary about his life and career which is released in cinemas on Friday.
Earlier this year, Kyrgios opened up about his own struggles with depression and self-harming, saying the 2019 Australian Open was one of his "darkest periods".
On court during Wimbledon, he was given a code violation during the final.
McEnroe had called Kyrgios' behaviour embarrassing and conceded that it could be seen as "the pot calling the kettle black", given the American's own arguments with umpires during his career.
Of his own antics, McEnroe said "there's certain behaviour that I regret", adding: "I would say I'm proud of most of what I did but there are certainly times where I'm like, 'I didn't need to do that'.
"It only exacerbated the situation and made more people get mad at me or start booing me so it wasn't like it helped me.
"It may be at times you blow off some steam. Obviously, you see Kyrgios doing that all the time. "
'If it wasn't so sad it would be funny'
Much of Kyrgios' on-court frustration was aimed at his own support box and McEnroe lamented that behaviour in particular.
"Most of what he does, I like," the three-time Wimbledon champion said.
"How do you think his box feels when he's screaming at them? Those are the people that love him most right?
"Unfortunately, the people that you love most you take it out on, because you feel closest to them. I think we can all relate to that. But if it wasn't so sad it would be funny in a way.
"So that part, hopefully he would look at and go, 'I don't need to do that to my dad or my girlfriend'."
McEnroe discussed his own psychological wellbeing, saying at one point he had "a feeling of doom" and that "of course" he wishes he had known more about mental health.
The 63-year-old said he has seen "plenty of sports psychologists" some of whom were "court ordered" because of "difficulties" with his ex-wife.
He added: "There's plenty of other people who have gone through it in a lot of other sports and maybe worse than me, but it did feel a bit overwhelming."