Fourteen-time major winner Woods is playing in the tournament for the first time in three years after recovering from a succession of back surgeries.
Woods, 42, transformed golf’s commercial appeal by dominating the sport in his early career and Player would like to see American return to his very best.
The 82-year-old said: “My big wish would be that he would win because Tiger Woods is responsible for these guys playing for a million every week.
“I think Tiger captures the young people, which we need in this game desperately at the moment. If he can bring this, it enhances the game and brings more young people into the game.
“He brings more people, the sponsors are delighted, the public are delighted and the media are delighted because you are still in awe of him.
“I think Tiger Woods will win another tournament and I hope he will win another major because we desperately need him to do that for the sake of the game. I sincerely hope he plays well.”
Player, however, feels there is downside to attracting more sponsors because some players are earning figures far exceeding their achievements.
The nine-time major winner said: “We wanted a man to play in our charity event at Wentworth one year – he wanted 500,000 dollars for the one day.
“We’ve got to be very careful that we don’t kill the goose that laid the golden egg. Managers have got to be realistic and realise that every golfer playing has a debt to society.
“Tiger Woods was paid millions of dollars. He deserved it because he was in a league of his own and he went there, brought the people in.
“But when you see an ordinary player who’s never won a major asking for 500,000 dollars or more, it’s a very sad day.”
Player was speaking at a specially-arranged press conference at Carnoustie to mark the 50th anniversary of the second of his three Open victories, which came at the Angus links.
Despite his wish for Woods to win, the South African accepts this week’s tournament is wide open.
He said: “The way the golf course is set at the moment, as the conditions are, anybody who plays in this tournament could win.”
Fittingly it was Padraig Harrington, the winner the last time Carnoustie hosted the Open in 2007, who best summed up the challenge in trying to identify who will hold the Claret Jug aloft on Sunday.
“I’m not sure if this is going to be the toughest Open ever or the easiest Open,” said Harrington, who defeated Sergio Garcia in a play-off 11 years ago and then defended the title at Royal Birkdale the following year.
The reason for Harrington’s dilemma is the unusual state of the course, which is playing so hard and fast that the three-time major winner drove into the Barry Burn in front of the 18th green in practice – and he was far from alone in reporting prestigious feats of distance.
That brings bunkers which may not usually be in play into the equation and as world number two Justin Thomas admitted, the bunkers at Carnoustie are “truly a water hazard. You can never hit it on the green from them.”
However, the greens themselves have been watered and are currently receptive, leading to the possibility – as at Gullane for last week’s Scottish Open – of a host of low scores, highlighted by Brandon Stone’s closing round of 60 which gave the talented South African a place in the Carnoustie field.
It all seemingly adds up to a choice between a conservative strategy and a more attacking approach, with the likes of Rory McIlroy and Jon Rahm taking their chances off the tee in the knowledge that the heatwave has also burned off some of the usually thick rough.
“I guess the risk of hitting the driver on a few holes is not having full control of your golf ball if it does run into the rough,” McIlroy, the 2014 winner, said.
“But the amount of gorse bushes that they’ve taken away from this golf course since 2007 [means] you’ve still got another five to 10 yards either side of the fairway where it’s okay.
“I think with links golf you have to adapt. I think there’s not going to be one player in this field that has a game plan on Wednesday night and is going to stick to that game plan the whole way around for 72 holes.
“The golf course is playing so firm and fast there’s some guys that will see it completely different than the way I see it. It’s going to be really interesting to see how it all plays out.”
McIlroy is approaching a fourth year without a major title, his last victory coming in the 2014 US PGA, a month after he won the Open at Royal Liverpool.
And although he has finished fifth and fourth the last two years, the 29-year-old could face a tough task to end the overseas dominance of golf’s biggest prizes, with American players holding the four major titles and teams from the United States in possession of all the transatlantic team trophies.
Jordan Spieth’s last victory was his triumph at Royal Birkdale 12 months ago, but the likes of world number one Dustin Johnson, Masters champion Patrick Reed and double US Open winner Brooks Koepka are part of a strong American challenge at Carnoustie.
And throw a certain Tiger Woods into the mix, in conditions reminiscent of his last Open victory at Hoylake in 2006, and Sunday’s winner will truly have earned the title of “Champion Golfer of the Year.”
— PGA TOUR (@PGATOUR) July 17, 2018
Ahead of the start of The Open Championship on Thursday, we look at three dark horses who could upset the odds.
Who do you think will win?
The two-time major winner has posted one top-five and six top-10 finishes this season. And although he has yet to contend for any titles, his game always remains in top shape through the year. At 42, the gritty Georgia man still has buckets of playing ability in him and enters this weekend ranked 20th in the scoring average. Could be a threat on the fast greens of Carnoustie this weekend.
Last five tournaments: T57-T13-MC-5-T21
The American has been superb this season, with top-10 finishes in the two major events this year – T10 at Augusta and fifth at Shinnecock Hills. In nine major tournaments, the Utah native has missed the cut twice, with neither coming at his two previous Open Championship appearances in 2016 and 2017. His overall record in 2018 is rock solid, recording four top-10s and five top-25s in 15 starts, including second place at the Genesis Open. If he can gather some momentum, he could take over the fast greens with his powerful game.
Last five tournaments: 1-2-T25-1-T2
The Italian has rediscovered his form this year and looks one of the best-placed players heading into this year’s Open. The 35-year-old has posted five top-25s and two top-10s, including wins at the BMW PGA Championship and Quicken Loans National. Although he has only managed three top-10s in 36 major starts, this could be the year when Molinari kicks into gear and mounts a strong challenge. Sergio Garcia won his first major at 35, so what’s stopping the Turin man from achieving the same feat?