Kyrgios, who fell to Novak Djokovic (35) in an engrossing final on Sunday, was asked by Hewitt to join the Australian squad for the men's team competition earlier this year but he declined.
"We'd absolutely love to have him playing for us," Hewitt, a two-time major champion who will be inducted into the International Tennis Hall of Fame on Saturday, told Reuters.
"We're a much stronger side if he's available and can play for us. And he's an option for singles and doubles matches, which is important in this format."
Kyrgios and countryman Thanasi Kokkinakis won the Australian Open doubles title in January.
"To have that kind of weapon at your disposal, we'd certainly want him to be part of that if possible," Hewitt said.
Kyrgios's thundering serve, his superb shot-making and hot temper have combined to make him one of the sport's most captivating players.
"Deep down he's still pretty disappointed to come so close but not win," Hewitt said.
"But as I told him, he should be extremely proud of the performances over the last two weeks and throughout the whole grasscourt season.
"Everyone knows the kind of firepower and game style that he has and what he's capable of doing. He just has to go out there and keep believing in himself."
Hewitt, who was also captain when Kyrgios was on the Davis Cup team in 2019, said that the combustible star probably does not need a full-time coach.
But would Hewitt ever consider taking on the challenge of coaching Kyrgios, who berated his box from the court during the final?
"Well I can't do it at the moment anyway because I'm Davis Cup captain, so the decision is easy right now," he said with a laugh.
HALL OF FAME
Not long ago it was Hewitt who was considered as the bad boy of tennis as he had a number of ugly run-ins with umpires.
Before Kyrgios even came into the spotlight, Hewitt used to go into battle by wearing his baseball cap backwards and punctuated points with emphatic fist pumps and cries of "C'mon!"
When he beat David Nalbandian in the 2002 Wimbledon final, it was the first time since 1978 that the men's showpiece match at the All England Club had been contested by two baseliners.
Being part of a generation who preferred grinding out points from the baseline instead of rushing to the net after serving, the success he enjoyed paved the way for the near extinction of the serve-and-volley game.
"It wasn't just me but because I was at the top of the game, it made it stand out more," he said.
"In that same era you had the likes of Juan Carlos Ferrero and Marat Safin and a lot of those guys would stay back and play from the baseline.
"Roger (Federer) took it to a new level and he was the greatest."
The Adelaide native won the first of 30 ATP titles aged 16, beat Pete Sampras to capture the 2001 U.S. Open, added a Wimbledon title the following year, spearheaded Australia to two Davis Cup triumphs and spent a total of 80 weeks as the world No. 1.
And now he can add being a Hall of Famer to his impressive resume when he is formally inducted this weekend in Newport, Rhode Island.
"It's a huge honour," he said.
"It was always something that I thought was a place for all the idols that I looked up to, not something that I ever thought I'd be inducted into."
